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ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS

VOLUME 79

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS

VOLUME 79

EDITOR-IN-CHIEF

PETER W. HAWKES Laboratoire d 'Optique Electronique du Centre National de la Recherche Scientijique Toulouse, France

ASSOCIATE EDITOR

BENJAMIN KAZAN Xerox Corporation Palo Alto Research Center Palo Alto, California

Advances in

Electronics and Electron Physics EDITEDBY PETER W. HAWKES Laboratoire d 'Optique Electronique du Centre National de la Recherche ScientiJique Toulouse. France

VOLUME 79

ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers Boston San Diego New York London Sydney Tokyo Toronto

This book is printed on acid-free paper.

@

COPYRIGHT 01990 BY ACADEMIC PRESS,INC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER.

ACADEMIC PRESS, INC. l2SO Sixth Avenue, San Diego, CA 92101

United Kingdom Edition published b y ACADEMIC PRESS LIMITED 24-28 Oval Road. London NWI 7DX

LIBRARYOF CONGRESS CATALOG CARDNUMBER: 49-7504 ISSN 0065-2539 ISBN 0-12-014679-7 PRINTED IN THE UNITED STATES OF AMERICA

90 91 92 93

9 8 7 6 5 4 3 2 1

CONTENTS C O N T R I B U T O R.S.. ,. . . . . . . . . . . . . . . . . . . . . . . . . . . . .................................... PREFACE

Algebraic Systems. Trellis Codes. and Rotational Invariance HOWARD J . CHIZECKAND MITCHELL D . TROTT I. I 1. 111. IV. V. VI . VII . VIII .

I. I1. 111. IV .

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Review of Modulation and Coding . . . . . . . . . . . . . . . Trellis Codes: Structure . . . . . . . . . . . . . . . . . . . . . . . Designing Trellis Codes . . . . . . . . . . . . . . . . . . . . . . . Finite Group Homatons . . . . . . . . . . . . . . . . . . . . . . . Rotational Invariance . . . . . . . . . . . . . . . . . . . . . . . . Finding New Codes . . . . . . . . . . . . . . . . . . . . . . . . . . Open Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii ix

1

2 4 18 28 37 51 64 69 70

Topography of Solid Surfaces Modified by Fast Ion Bombardment 73 D . GHOSEAND S. B . KARMOHAPATRO Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Basic Ion Bombardment Processes . . . . . . . . . . . . . . . . . . 76 Ion-Induced Surface Modifications . . . . . . . . . . . . . . . . . . 82 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

Scanning Tunneling Microscopy: A Mature Surface-Science Technique L . L . SOETHOUT. H . VAN KEMPEN. G . F . A . VAN DE WALLE I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1 . Modes of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Construction and Electronics . . . . . . . . . . . . . . . . . . . . . IV . Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V . Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V

155

156 157 168 188 203

vi

CONTENTS

VI . Related Scanning Techniques and Spin-off . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I. I1. I11. VI . V. IV . VII . VIII . IX .

X.

..

Phosphor Materials for Cathode-Ray Tubes NAKAZAWA. TAKASHI HASE.TSUYOSHI KANO.EIICHIRO AND HAJIME YAMAMOTO Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Luminescent Processes of Phosphors . . . . . . . . . . . . . . . Cathode-Ray Excitation Processes . . . . . . . . . . . . . . . . . Phosphor Materials for Specific Applications . . . . . . . . . . . Methods Used for Synthesis of Phosphor Powders . . . . . . . Screen Fabrication Techniques . . . . . . . . . . . . . . . . . . . Special Phosphor Screens . . . . . . . . . . . . . . . . . . . . . . Phosphor Aging . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contrast-Enhancing Techniques in Color Tubes . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix 1. Characteristics of Widely Used Phosphors for Main Categories of Cathode-Ray Tubes . . . . . . . . . . . . . . Appendix 2. Relative Spectral Distribution Curves of Cathodoluminescence Emission for the Phosphors Listed in Appendix I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

INDEX.

.....................................

246 257 257

271

272 273 289 307 325 332 337 349 353 356 358 359 361 365

373

CONTRIBUTORS The numbers in parentheses indicate the pages on which the authors’ contributions begin.

HOWARD J. CHIZECK (l), Department of Systems Engineering, Case Western Reserve University, Crawford Hall 612C, 10900 Euclid Avenue, Cleveland, Ohio 44106. D. CHOSE (73), Saha Institute of Nuclear Physics, Sector 1, Block AF, Bidhan Nagar, Calcutta 700 064, India TAKASHI HASE (271), Technical Department, Kasei Optonix Ltd., 1060, Naruta, Odawara, Kanagawa 250, Japan TSUYOSHI KANO (27 l), Central Research Laboratory, Hitachi Ltd., P.O. Box 2, Kokubunji, Tokyo 185, Japan S. B. KARMOHAPATRO (73), Saha Institute of Nuclear Physics, Sector 1, Block AF, Bidhan Nagar, Calcutta 700 064, India EIICHIRO NAKAZAWA (271), Electronic Engineering Division, Kogakuin University, Nakano-cho, Hachioji, Tokyo 192, Japan L. L. SOETHOUT (155), Research Institute for Materials, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands MITCHELL D. TROTT (l), Department of Electrical Engwieering, Stanford , University, Stanford, California G. F. A. VAN DE WALLE (155), Philips Research Laboratory, Building WAM, 5600 JA Eindhoven, The Netherlands H. VAN KEMPEN (155), Research Institute for Materials, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands HAJIME YAMAMOTO (271), Central Research Laboratory, Hitachi Ltd., P.O. Box 2, Kokubunji, Tokyo 185, Japan

vii

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PREFACE The four chapters in this volume are divided among two new and rapidly developing themes and two more traditional topics. We open with an account of trellis codes and related material, a subject which is of interest in the abstract field of coding and no less in many applied fields where datacompaction, such as digital image storage, is desperately needed. Over the past years, the quest for new types of code has intensified, and the challenge of finding ways of using vector codes, known to permit high compression ratios, without the inconvenience of huge codebooks has stimulated much interesting work. This account of trellises is a very welcome addition to these Advances. The next two chapters are devoted to surfaces but have little else in common. In the first, D. Chose and S. B. Karmohapatro survey the effects caused by bombarding surfaces with ions. The other surface-related chapter is the first in these Advances to be devoted to the scanning tunnelling microscope, which has been phenomenally successful since it was introduced only a few years ago. The authors, L. L. Soethout, H. van Kempen and G. F. A. van de Walle, have written a very up-to-date account, including many recent findings, and I am confident that this chapter will be widely used. I am no less certain that an updated version will be needed soon, for the subject is in rapid evolution. The closing chapter, by T. Hase, T. Kano, E. Nakazawa and H. Yamamoto, is concerned with one of the oldest types of electronically-active materials. As early as 1987, the practical importance of such phosphors was recognized when F. Braun demonstrated that luminescent powder layers of some naturally-occurring minerals could be used as the screen for the first cathoderay tubes. Since then, the continuing study and synthesis of new phosphors has played a major role in enabling cathode-ray tubes to reach their dominant position in the display field. This situation is hardly surprising in view of the enormous number of characteristics obtainable with modern phosphor materials. These can be tailored, for example, to emit light in almost any portion of the visible spectrum, and can be prepared with decay times spanning the range between about a tenth of a microsecond and several seconds. Of major importance is the fact that many phosphors are available with energy conversion efficiencies as high as 10-20%. Despite the extensive body of literature which has accumulated on this subject, no comprehensive survey appears to have been written during the past few decades. It is thus believed that the present chapter will be welcomed by workers in this area. ix

X

PREFACE

Among the various topics covered are the basic luminescent processes (Section 11); electron-beam excitation processes (Section 111); materials for specific applications (Section IV); the synthesis of phosphor powders (Section V); screen deposition techniques (Section VI); special types of screens (Section VII); phosphor aging (Section VIII); and contrast-enhancing techniques (Section IX). It only remains for me to thank all the contributors most warmly and to list forthcoming chapters. I am always pleased to receive proposals for contributions to the series, in any of the many fields of electronics and electron physics, including digital image processing and analysis. Peter W. Hawkes

FORTHCOMING ARTICLES Image Processing with Signal-Dependent Noise Parallel Detection Pattern Recognition and Line Drawings Bod0 von Borries, Pioneer of Electron Microscopy Magnetic Reconnection Vacuum Microelectronic Devices Sampling Theory Electrons in a Periodic Lattice Potential The Artificial Visual System Concept Image Analysis and the Wigner Distribution Speech Coding Corrected Lenses for Charged Particles The Development of Electron Microscopy in Italy The Study of Dynamic Phenomena in Solids Using Field Emission Pattern Invariance and Lie Representations Amorphous Semiconductors Median Filters

H. H. Arsenault

P. E. Batson H. Bley H. Von Borries A. Bratenahl and P. J. Baum 1. Brodie and C. A. Spindt J. L. Brown J. M. Churchill and F. E. Holmstrom J. M. Coggins G. Cristobal, C. Gonzalo and J. Bescos V. Cuperman R. L. Dalglish G. Donelli M. Drechsler M. Ferraro W. Fuhs N. C. Gallagher and E. Coyle

xi

PREFACE

Bayesian Image Analysis Discrete Fast Fourier Transfer Algorithms and Multiplicative Fast Fourier Transfer Algorithms Number Theoretic Transforms Applications of Speech Recognition Technology Spin-Polarized SEM Analysis of Potentials and Trajectories by the Integral Equation Method The Rectangular Patch Microstrip Radiator Electronic Tools in Parapsychology Image Formation in STEM Information Energy and Its Applications Low Voltage SEM Z-Contrast in Materials Science Languages for Vector Computers Electron Scattering and Nuclear Structure Electrostatic Lenses Energy-Filtered Electron Microscopy CAD in Electromagnetics Image Algebra Scientific Work of Reinhold Riidenberg Metaplectic Methods and Image Processing X-Ray Microscopy Accelerator Mass Spectroscopy Applications of Mathematical Morphology Optimized Ion Microprobes Focus-Deflection Systems and Their Applications Electron Gun Optics Thin-Film Cathodoluminescent Phosphors Electron Microscopy and Helmut Ruska Parallel Imaging Processing Methodologies

S. and D. Geman I. Gertner G. A. Jullien H. R. Kirby K. Koike G. Martinez and M. Sancho

H. Matzner and E. Levine R. L. Morris C. Mory and C. Colliex L. Pardo and I. J. Taneja J. Pawley S. J. Pennycook R. H. Perrot G. A. Peterson F. H. Read and I. W. Drummond L. Reimer K. R. Richter and 0. Biro G. X.Ritter H. G. Rudenberg W. Schempp G. Schmahl J. P. F. Sellschop J. Serra Z. Shao T. Soma

Y. Uchikawa A. M. Wittenberg C. Wolpers S. Yalamanchili

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ADVANCES 1N ELECTRONICS A N D ELECTRON PHYSICS. VOL. 19

Algebraic Systems. Trellis Codes. and Rotational Invariance HOWARD J . CHIZECK Department o j Systems Engineering Case Western Reserve Unioersity Cleoeland Ohio

.

MITCHELL D . TROTT* Department of Electrical Engineering Stanford University Stanford. California

1. Introduction . . . . . . . . . . . . . . 11. A Review of Modulation and Coding . . . . . A . Error-Correction Codes . . . . . . . . . .

. . . . .

B. The Binary Symmetric Channel . . . . . . . C . TheModulator . . . . . . . . . . . . . . D. ChannelNoise . . . . . . . . . . . . . . E. The Demodulator . . . . . . . . . . . . . F. TheDecoder . . . . . . . . . . . . . . . G . Constellations . . . . . . . . . . . . . . H . Performance Measurement . . . . . . . . . 1. TheEncoder . . . . . . . . . . . . . . . 111. Trellis Codes: Structure . . . . . . . . . . . . A . Trellis Codes . . . . . . . . . . . . . . B. Trellis Diagrams . . . . . . . . . . . . . C . Finite and Infinite Input Memory Systems . . . D . Equivalence and Minimality . . . . . . . . E . Catastrophic Error Propagation . . . . . . . IV . Designing Trellis Codes . . . . . . . . . . . . A . Viterbi Decoding . . . . . . . . . . . . . B. Calculating Free Euclidean Distance . . . . . C . Heuristic Code Design . . . . . . . . . . . D. Code Design by Enumeration. . . . . . . . V . Finite Group Homatons . . . . . . . . . . . . A . Finite Group Homatons. . . . . . . . . . . B. Weighting Patterns . . . . . . . . . . . . C. Initial State . . . . . . . . . . . . . . . D . Minimality and Transient States . . . . . . .

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5

7 10 11

12 12

. . . . . 15 . . . . 17 . . . . 18 . . . . 18 . . . . 19 . . . . . 21

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2 4 4

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. . . . . 27 . . . . 28 . . . . 29 . . . . . 31 . . . . 32 . . . . . 35 . . . . 37 . . . . 38 . . . . 40 . . . . 42

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42

*This material is based upon work supported under a National Science Foundation Graduate Fellowship. Copyright 0 1990 by Academic Press. Inc . 1

All rights of reproduction in any form reserved. ISBN 0-12-014679-7

2

HOWARD J. CHIZECK AND MITCHELL D. TROTT

E. InverseSystems. . . . . . . . . . . . . . . . F. CatastrophicCodesand Infinite Input Memory Systems G. Realizability. . . . . . . . . . . . . . . . . V1. Rotational Invariance, . . . . . . . . . . . . . . A. Carrier Phase Tracking and Synchronization . . . . B. Rotationally Invariant Trellis Codes . . . . . . . C. Differential Encoding. . . . . . . . . . . . . . D. FGH Rotational Invariance . . . . . . . . . . VII. Finding New Codes . . . . . . . . . . . . . . . VIII. Open Questions. . . . . . . . . . . . . . . . . References. . . . . . . . . . . . . . . . . . .

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46 47 48 . . . 51 . . . . 52 . . . . 53 . . . 55 . . . . 57 . . . 64 . . . 69 . . . 70

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I. INTRODUCTION In this work we apply algebraic systems theory to coding theory. A major goal of coding theory is the design of error-correction codes, a type of code used to transmit information reliably over an unreliable medium. Difficult questions about code design can often be answered by representing codes in an algebraic setting. For example, by representing convolutional codes as linear sequential circuits (LSCs), Forney (1970) showed that any convolutional code is “equivalent” to an LSC in a relatively small canonical class. Convolutional codes are designed largely by enumeration; Forney’s results transformed a computationally impossible search into a simple one. Here, we are interested in trellis codes, a kind of error-correction code for continuous bandlimited channels. A trellis code is a finite state machine (the encoder) whose outputs select points from a finite constellation of points in ndimensional Euclidean space. Ideally, we’d like a constructive technique that produces “good” trellis codes for arbitrary constellation, state, and input sets. But at present this isn’t possible, in part because the performance of a trellis code depends in a complicated way on interactions between the encoder and the constellation. We can, however, find good trellis codes through enumeration: Select a constellation and a set of encoders, then sift through the encoders to find the ones that work best. The problem is to choose a class of encoders with enough structure to allow rapid enumeration, yet enough generality to include useful codes. Binary convolutional codes (linear sequential circuits) are typically used as the search class. They are easily enumerated, and their structure allows the formulation of a priori rejection rules. For example, simple rules can be used to insure that no catastrophic codes are considered in a search (Massey and Sain, 1967, 1968). But not all useful trellis codes are convolutional. In particular, a more general setting is needed to describe rotationally invariant codes and codes with nonbinary state and constellation sizes.

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

3

In this paper we use a new class of algebraic systems called j i n i te group hornatons (FGHs) (Karpen, 1986) to describe trellis codes. FGHs are a generalization of linear sequential circuits, yet they retain enough structure to allow enumeration. Many codes that are not convolutional can be modeled as FGHs. For example, Wei’s (1984) 8-state 32-CR 4-way rotationally invariant nondifferentially encoded trellis code is easily represented as an FGH, while it cannot be described as a linear sequential circuit. Other mathematical models for analyzing trellis codes have been proposed by Calderbank and Mazo ( I 984), Calderbank and Sloane (1987), and Ungerboeck (1982), but these models stress mainly quantitative issues, such as asymptotic performance bounds and error rate calculation. FGHs are interesting because the group structure of the output can be chosen to align with the symmetries of the constellation. With LSCs, for example, the output elements are assigned to points (or partitions) in the constellation in an arbitrary manner. A geometric interpretation of the symmetries in the output group is central to our results on rotational invariance. The development of new tools for the construction and analysis of trellis codes is of some practical importance. Since their introduction by Ungerboeck (1982), trellis codes have proven effective in a wide range of applications from satellite communications to high speed modems. Recently, Wei’s (1984) rotationally invariant trellis code was adopted as an International Telegraph and Telephone Consultative Committee (CCITT) standard for 9600 bit/s voiceband communication. Throughout our presentation we focus mainly on the structure of the encoder, rather than on the constellation. See Forney (1988) for a thorough treatment of recent advances in constellation design. In Section I1 we introduce notation and concepts related to error-correction coding and trellis codes. Section 111 addresses the structural aspects of trellis codes. Trellis codes are precisely defined, diagramming techniques are explained, and the concepts of equivalence, minimality, and finite input memory systems are introduced. The material in Sections 111-TV is a formalization of important concepts only vaguely stated in recent coding literature, based upon Trott (1988). Section IV focuses on the error-correcting functions of trellis codes. The techniques used for maximum likelihood decoding, calculation of free Euclidean distance, and heuristic code design are briefly reviewed. The mathematical frameworks used by previous authors as an aid to analysis and enumeration are examined in light of the material from Section 111, with emphasis on the range of trellis structures these settings are able to represent. In Section V we review prior results and present several new results on the structure and behavior of FGHs, focusing on their relevance to trellis codes. In Section VI we apply these results to provide necessary and sufficient conditions for an FGH trellis code to be rotationally invariant (rotational

4

HOWARD J. CHIZECK AND MITCHELL D. TROTT

invariance is exclusively nondifferentially encoded; i.e., no precoder). In Section VII we show how to find new trellis codes using FGHs. Several new codes are presented, including rotationally invariant codes for 8- and 12-PSK constellations. One particularly interesting code is a 16-state eight-way rotationally invariant code that has the same performance as Ungerboeck’s 8-state code.

11. A REVIEW OF MODULATION AND CODING In this section we present an informal introduction to modulation and error-correction coding. The material here is largely a synthesis of results from other sources, particularly Biglieri (1 984), Forney et al. (1984), Ungerboeck (1982,1987) and Wilson et al. (1984). It is intended as a review. A . Error-Correction Codes The problem of error-correction code design is to achieve reliability as efficiently as possible. However, efficiency and reliability are defined in terms of the application. Code design involves a tradeoff among error resistance, hardware complexity, and bandwidth requirements for the encoded data. The first error-correction codes were introduced by Hamming in 1948 to improve the reliability of mechanical relay computers (Thompson, 1983). Before Hamming’s work, codes were used only to detect errors, not to correct them. Each detected error brought the computer to a grinding halt; full-time operators stood by to fix the error and restart the system. Today, errorcorrection codes are used whenever information must be transmitted or stored reliably . As shown by Shannon (1948), near-perfect reliability is possible in most cases, as long as the data are not transmitted too quickly or packed too densely on the recording medium. A simplified coding scheme is shown in Fig. 1. Information, usually in digital form, is generated at the source, encoded, and then sent through a noisy channel. The decoder must reconstruct the original information, which is passed to the sink.

Sink

FIG.I , Block diagram of a simple coding scheme.

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE 5

All codes work by adding redundancy to the data, but this redundancy can be used in different ways. Automatic retransmission request (ARQ) codes use redundancy only to detect errors. When an error is found, a repeat transmission is requested. This requires a bidirectional communication channel, as indicated by the dashed return path in Fig. 1. Forward error correction (FEC) codes, on the other hand, use the redundant information to correct errors at the decoder. Only a one-way communication path is needed. The relative merits of FEC, ARQ, and combined coding methods are discussed in Berlekamp et al. (1987). We are concerned only with FEC codes here.

B. The Binury Symmetric Channel Two common uses of error correcting codes, compact discs and satellite channels, require vastly different coding methods. One reason is that storage on a CD is inherently digital, while a satellite channel is continuous. With a digital channel, errors are simple. Data are transmitted (or stored) as a sequence of binary digits, or hits. Each bit either is received correctly, or isn't. One usually assumes that the probability of an error for any bit, the bit error rate (BER), is some constant p , and that an error at one bit is independent of errors at any other bits. This type of structure, shown in Fig. 2, is called a binury symmetric channel. Examining a sequence of n received bits, assuming that np << 1 - p , the most likely event is that all bits are received correctly. This occurs with probability ( 1 - p)". The next most likely event is a single error, occurring with probability np(1 - p ) " - ' . In general, the probability of r errors in n bits is binomially distributed:

Pr{r errors in n bits)

=

(3

pr(l - p)"-'.

(1)

The simplest way to lower the BER of a binary symmetric channel is to eliminate the possibility of up to r errors in any string of n bits. The following classic example of a single-error correcting code (from Thompson (1983)) shows how this is done for r = 1 and n = 4.

-j:x:k FIG.2 . The binary symmetric channel.

6

HOWARD J. CHIZECK AND MITCHELL D. TROTT

Example: Hamming's rate (7,4) single-error correcting binary block code, one of the first codes developed, operates as follows. First, the input is broken up into blocks of four bits called 4-blocks. Label the sequence of input blocks uk for k = 0, 1 , 2 , .. . . The output of the encoder in response to an input 4block uk is a 7-block yk. In general, an encoder with m-block inputs and n-block outputs is described as a rate (n, m) code, where n must be greater than m for the encoder to add redundancy. The four bits of the input block, the information bits, appear unchanged in the output 7-block. Specifically, the mapping is [u1u2u3u4]

H [*

* u 1 * 212143214].

(2)

A code whose inputs appear in the output is called systematic.

The remaining three bits of yk, the check bits, are chosen such that

E 8 p ; 1 ; i].+].

(3)

For example, uk = [l 0 1 01 maps to yk = [ l 0 1 1 0 1 01, where the information digits are underlined. The 3 x 7 matrix, usually identified with the letter H, is called a parity check matrix. The values of yk that satisfy Eq. ( 3 ) are called code words. They are just the elements of the null space of H. Note that the modulo 2 sum of any two codewords is another codeword. A code with this property is said to be linear. Each bit of yk is sent along the channel; label the received 7-blocks y k . The decoder operates in two steps. First, the syndrome Sk of y k is calculated as (4)

S, = H F l .

If yk = y k , then S,T = [O 0 01 and the information digits are immediately extracted. If yk and yk differ in one position, then Sk indicates (in binary) the location of the error in y k . For instance, if yk=[1

0 1 1 0 1 01

and

y k = [ 1

0

1

1

0 0 01

(5)

then

The error is in column 2'(1) + 2'(1) + 2'(0) = 6. The syndrome locates any single error regardless of the column. However, if Y k and differ in more than one position the decoder will behave unreliably.

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

7

Hamming’s code eliminates the possibility of single-bit errors, but the price is a decrease in transmission speed. The encoder produces seven bits rather than four, so the transmission rate is 4 input bits per output bit. Also, the chance of a single-bit error in seven bits is greater than in four, so the decrease in BER is not as large as might be expected. Furthermore, if more than one error occurs then the decoder may “correct” the wrong bit and compound the fa i I u re. More complex codes can correct more errors. As the block sizes n and m grow large, reliability is limited only by Shannon’s (1948) channel capacity C, a function of the noise statistics of the channel. If information is transmitted at a rate lower than the channel capacity, i.e., m / n < C, then perfect reliability is (asymptotically) possible. At a rate higher than C, reliable transmission is impossible. For the binary symmetric channel,

c = 1 + plog,p + (1 - p)log,(l - p).

(7)

When p = 9, Eq. (7) gives C = 0, an intuitively satisfying result. Unfortunately, Shannon’s results are statistically derived. They tell only that a capacity utilizing code exists, not how to build it. Moreover, the capacity C is a theoretical upper bound, not a practical one. For certain codes (Jacobs and Berlekamp, 1967), the mean and variance of decoding time becomes infinite before the channel capacity is reached. C. The Modulator

Binary symmetric channels are popular not only because they occur commonly in practice, but also because they are relatively easy to analyze. C o d n u o u s channels, however, present a more difficult problem. The block diagram of a typical FEC coding scheme for a continuous channel is shown in Fig. 3. Even with a continuous-time continuous-valued channel, the encoder is still discrete. The modulator converts the discrete encoder outputs into a continuous channel signal. There are many types of modulators; we are concerned with linear memoryless modulation. The input to a linear modulator is a sequence of p-dimensional vectors. These vectors come from a “mapper,” which converts each encoder output y k E Y into a distinct vector ak E R P .That is, ak = M(yk),

M :Y -S R P ,

(8)

where Y is the finite output alphabet of the encoder. Each ak is called a signal point. The collection of all signal points, the image of M(.), is called the p dimensional constellation or signal sef. The name comes from the graphical

8

HOWARD J. CHIZECK AND MITCHELL D. TROTT

Modulator

I

recovered

information

Parallel to Serial

*

. '

ak

Decoder

i

Demodulator

6

representation of the signal points when p = 1 or 2, as in Fig. 4. The signal points are normally labeled with the elements of Y to indicate the mapping M ( . ) implicitly. The modulator forms the channel signal z ( t ) ~ Rby taking a linear combination of the components of a p-dimensional real-valued basis function $(t) E RP: z ( t ) = af+(t)

for

Tk I t < T(k + 1).

(9)

The components of the basis function are mutually orthogonal:

+

for i, j = 1,2,. . . ,p and i j, where 4i(t) is the ith component of $(t). Mutual orthogonality allows the signal points to be recovered from z ( t ) at the demodulator (see Section 1I.E). The time interval T is called the modulation interval. The channel signal during one modulation interval is called a channel symbol. Note that a discontinuity in z ( t ) is possible at t = Tk. The modulation interval T, constellation dimensionality p , and basis function 4(t)are normally chosen to satisfy hardware constraints (Wilson et a/., 1984). These constraints include bandwidth limitations, restrictions on modulator complexity, and the desired speed of operation. We will assume here that they are prespecified. Even with simple choices of 4(t),the frequency spectrum of the channel signal can be difficult to compute (see Biglieri, 1986). The above modulation technique is considered memoryless because the channel signal during time interval [Tk, T ( k + 1)) depends only on y,. Modulation techniques with memory, such as continuous phase modulation

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

9

cos wt

<

-

-

I

sin wt

t

-- - -

'

-

1

-

'I' (d)

:

-

- c

+

' (el

FIG.4. One- and two-dimensional constellations: (a) 2-AM (amplitude modulation), (b)4-AM, (c)%AM,(d) 16-QASK (quadrature amplitude-shift keying), (e)2-PSK or BPSK (binary phase-shift keying), (f) 4-PSK or QPSK (quaternary phase-shift keying), (9) 8-PSK.

(CPM) (Aulin and Sundberg, 1981a, 1981b) and post-modulation filtering (Biglieri, 1984), can be used to prevent discontinuities in z ( t ) and thereby narrow the signal bandwidth. However, such techniques greatly complicate code design. Linear memoryless modulation hides the continuous-time nature of the channel. From the encoder's perspective, all choices of T and 4(t)appear equivalent: the encoder/mapper can only choose real vectors to send along the channel, not arbitrary functions. The only relevant factors are the channel noise statistics and the dimensionality of the constellation. A continuous channel constrained in this way is called a discrete memoryless channel (DMC).

10

HOWARD J. CHIZECK AND MITCHELL D. TROTT

The number of dimensions in a particular DMC‘s constellation is somewhat flexible. Because each component of the vector ak can be selected independently, a 2p-dimensional constellation can be trivially separated into two p-dimensional constellations driven by independent encoders. Conversely, a p-dimensional constellation can be converted to a 2p-dimensional constellation by merging consecutive channel symbols. For example, 4(t) = sin wt could be replaced by [shot

OIT

0 It < T, T1t<2t

with the new modulation interval T* = 2T. For a given T, constellations with many dimensions are able to transmit information more rapidly than those with few. However, increasing the number of dimensions in a constellation proportionately increases the bandwidth of the channel signal. For this reason, the capacity of a channel is measured in bits per dimension rather than as a unitless quantity. For example, Hamming’s (7,4) code could be said to have rate $ inputs bits per output bit. However, the sequence of seven output bits corresponding to seven consecutive uses of a binary symmetric channel can be viewed as a sevendimensional constellation, as in Eq. (11). The rate now becomes 4 bits per dimension. If the sequence of seven output bits is mapped to a onedimensional constellation with 2’ points, the rate would be four bits per dimension. Rate is sometimes given in bits per symbol, which is the same as bits per two dimensions. The performance of two constellations with a differing number of dimensions can be sensibly compared only when their modulation intervals are equal.

D . Channel Noise The channel represents everything that happens to z(t) between the modulator and the demodulator. All forms of channel disturbance are referred to collectively as noise. Noise can include echo, fading, carrier phase slippage, burst noise, and harmonic distortion. To simplify analysis, one usually assumes that all noise is zero mean, additive, white, and Gaussian (AWGN). Noise is then described entirely in terms of its variance, which is proportional to its energy. Code performance under this idealized assumption is often comparable to that achieved in practice, particularly for bandlimited channels such as voice-grade telephone lines (Wilson et al., 1984). The lower the noise energy, the more reliable the channel. But lowering the noise energy is indistinguishable from increasing the power of the transmitted

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

11

signal. Noise is therefore measured in relative terms, as the signal-to-noise ratio (SNR) in decibels: SNR

=

20 log,,

(2),

where E, is the expected signal energy (see Eq. (1 8)) and En is the expected noise energy (variance). Using the SNR, Shannon’s channel capacity (see Eq. (7)) for a discrete memoryless channel is easily calculated as C = +log,( 1

+ EJE,)

bits/dimension.

(13)

E. The Demodulator The demodulator takes the received channel signal z ( t ) over each modulation interval and, using an “integrate and dump” algorithm (Wozencraft and Jacobs, 1965), separates the orthogonal components to form 4 . Due to channel noise, the demodulated vector i?k will not in general be a point from the transmitted constellation. Assuming AWGN yields i i k = ak + w k , where { w k } is a sequence of independent normally distributed zero mean random variables with variance o 2 in each dimension. The conditional probability density function of is, given ak is

where p is the dimensionality of the constellation. A hard-decision demodulator estimates ak based solely on Zk, then passes its estimate of ak to the decoder. In other words, the demodulator output is a point in the original constellation. From examination of Eq. (14), the maximum likelihood estimate of ak given Ck assuming AWGN is the signal point with the minimum Euclidean distance from ir,. This method, when used in the demodulator, is called the “nearest neighbor” algorithm. Note that binary phase-shift keying, or BPSK (Fig. 4e), combined with hard decision demodulation acts exactly like a binary symmetry channel. In fact, any constellation with 2” points when combined with hard-decision demodulation is similar to n parallel binary symmetric channels, provided that the encoder outputs are mapped to signal points in such a way that the most likely errors correspond to an error in a single bit. Hard-decision demodulation is optimal in the sense of minimizing bit error rate when the sequence of vectors { Z k } is uncorrelated, but the received vectors are uncorrelated only for the simplest of codes. When the i i k are

12

HOWARD J. CHIZECK AND MITCHELL D. TROTT

correlated, using a nearest neighbor algorithm at the demodulator destroys information useful to the decoder. A soft-decision demodulator, rather than “rounding off” to the nearest signal point, passes the received point to the decoder unchanged. Despite the increased complexity, virtually all modern coding schemes use soft-decision demodulation (Forney et al., 1984). In the above discussion, we have implicitly assumed perfect carrier phase tracking and synchronization. That is, both the modulator and demodulator have an absolute time base, and they agree on where each modulation interval starts. This is not possible in practice; the consequence of incorrect phase tracking is a “rotation” in the received signal constellation. Specially designed rotationally invariant codes help solve this problem. The analysis of rotationally invariant trellis codes using finite group homatons is addressed in Section VI. F. The Decoder

The decoder is usually the most complicated part of a coding scheme, especially when combined with soft decision demodulation. Only the recent availability of inexpensive computing power has made powerful coding schemes, such as trellis coding, commercially feasible. The structure of the decoder depends strongly on the type of code used, so we will not give a general description here. A trellis code maximum likelihood decoder is described in Section 1V.A. Sometimes, when the signal constellation and encoder have highly symmetric structures, a balance of hard- and soft-decision demodulation and decoding is used. The result is slightly suboptimal performance with a large reduction in decoder complexity (Wilson et al., 1984).

G. Constellations

Constellations are designed primarily for energy efficiency and error resistance. The transmission energy of a signal point a is proportional to

= Ilal12K

because of the orthogonality of the components of

4(t).The functions +(t) are

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

13

usually normalized so that the energy of a signal point is its squared Euclidean norm. Then, the peak energy E, and averuge energy E, of a constellation C are

where Pr(u) is the probability that the encoder selects point a at any time k. Using the common assumption that all points in C are used equally often,

where ICI is the number of points in C. Peak energy determines the cost of the final amplifier stage in the transmitter. In an effort to minimize peak energy, the points in a constellation are clustered around the origin. For purposes of comparison, constellations are always normalized to have equal average energy. Assume that successive encoder outputs are uncorrelated, so that harddecision demodulation is optimal. Assume also that channel noise is low, so that errors are rare. Then, mistaking a signal point for its nearest neighbor will be the most frequent type of decoding error (see Eq. (14)),and the closet two signal points will be responsible for the majority of errors. In this situation, the BER is minimized when the minimum distance between signal points is as large as possible. For a given average energy, constellation dimensionality, and number of signal points, finding the optimum constellation is a problem in packing spheres around the origin (Thompson, 1983). Perfect packing is neither possible nor necessarily desirable for several reasons. First, minimizing peak energy to reduce the cost of the transmitter and maximizing interpoint distance to minimize BER are conflicting goals. Second, when sequential channel symbols are correlated, an ideally packed constellation is not always optimal in the sense of minimizing BER for a given average energy. Finally, and perhaps most importantly, the demodulator and decoder can be considerably simplified when the signal points fall on a regular lattice (Forney et al., 1984). The number of points in a constellation and the constellation’s dimensionality are usually dictated by the application. Generally, constellations with more points and dimensions require somewhat less energy per bit to achieve the same error resistance as a constellation with fewer points and dimensions. As the number of points and dimensions becomes large the asymptotic performance gains range from 1 to 2 dB (Forney et al., 1984; Forney, 1988),but the price of increased efficiency is an increase in coding-system complexity. Despite their suboptimality, the same constellations used for uncoded modulation are often used even when combined with coding. Irregular

14

HOWARD J. CHIZECK AND MITCHELL D. TROTT

constellations give only small performance gains, increase decoder complexity, and behave unpredictably with certains types of non-Gaussian noise (Ungerboeck, 1987). They are not used widely in practice. Example: The quaternary phase-shift keying (QPSK or 4-PSK) constellation is depicted in Fig. 5, with 4(t)= [sinwtcoswt]. The value w is called the carrier frequency, and the sin wt and cos wt axes are called the inphase and quadrature, respectively. The elements of the encoder output alphabet Y = { a ,b,c,d} are mapped into the signal points (1,O) (0, I), ( - 1,O) and (0,- 1). The four possible channel symbols during each modulation interval are therefore a : sin wt = sin wt,

(

3 + ( 3

b: coswt =sin wt c:

-sin ot

+-

= sin(wt

,

n),

d : -coswt =sin w t f -

.

The origin of the name “phase-shift keying” is apparent. Because all signal points have the same magnitude, PSK is commonly used in satellite communications where channels are subject to fading. The automatic gain control circuitry used to correct fading distorts any amplitude information in the signal. Although &t) = [sin wt cos wt] is common, other possibilities include amplitude modulation (AM) with $ ( t ) = [sin ot], frequency-shift keying (FSK) with 4(t)= [sin ot sin 20x1, and combined methods. More elaborate schemes use signal points to specify discrete Fourier transform coefficients

d

t

(0.-1)

FIG.5. Quaternary phase-shift keying

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

15

(Ruiz and Cioffi, 1987); the modulator acts as an inverse DFT followed by a lowpass filter, allowing careful control of the output frequency spectrum. rn H . Pevformance Measurement

As discussed in Section ILA, codes work by adding redundancy to the input data. Hence, the output space of the encoder must be “larger” than the input space. Viewed as a discrete-time system, the cardinality of the output set Y must be greater than the cardinality of the input set U, i.e. I U I < I Y 1. With this condition, not every sequence of elements in Y can be produced by the encoder. When uncoded modulation is used, a decoding error occurs when one valid signal point is mistaken for another. With coded modulation, an error occurs when one valid output sequence (or block) is mistaken for another valid output sequence. To maximize error resistance, the allowed output sequences must as “far apart” as possible. Then, even after corruption by noise, output sequences will not be easily confused. The definition of distance depends on the type of channel. The metric for a binary symmetric channel is Humming distance, which is the number of bits in which two sequences differ. Formally, the Hamming distance between two binary sequences { u o , . . . ,u k } and { O n , . . . ,uk} is

where 0 denotes modulo two addition. With Hamming’s rate (7,4) block code, all 32 allowed output 7-blocks are separated by a distance of at least three bits. After a single-bit error, any output block can still be uniquely identified. For a continuous channel with AWGN, the distance between two signals y ( t ) and z ( t ) on the interval [0, t , ] is the L, norm, defined as D ( y ( 0 , 40) =

(1:’

Cy(t) - 40l2dt)’”.

For a discrete memoryless channel this becomes

(21)

16

HOWARD J. CHIZECK AND MITCHELL D. TROTT

where { y k }and { z k } are real-valued vector sequences corresponding to y ( t )and z(t). The free Euclidean distance of a code is the minimum distance between any two valid encoder output sequences (or blocks) { y k } , { z k } :

For an uncoded system, d l output sequences { y k } , { z k } are valid. Hence, dfree for an uncoded system is the distance between the closest two signal points. It follows from Eqs. (24)and (25) that if every point in a constellation is scaled in magnitude by a constant, dfreechanges proportionally. If the signal-to-noise ratio is high, the performance of a code is tightly bounded by the expression Pf(error) 2 N(d,ree)Q(dfree/2o),

(26)

where o 2 is the noise variance, N ( d f r e eis) the average number of sequences at distance dfreefrom any given sequence, and

Q(4=

lXm exp(-x2/2)dt.

(27)

For small codes and constellations the effect of N ( d f r e eis) negligible, but for large codes its effect must be carefully considered. Equation (26) indicates that codes should have a high d,,,, for best performance. Catastrophic error propagation, as defined in Section III.E, is an exception to Eq. (26). Different methods are used to calculate dfreefor different types of codes (Mulligan and Wilson, 1984); some sample calculations for trellis codes are given in Section 1V.B. Calculating free Euclidean distance is computationally difficult, but deriving the exact BER of a code is much harder. Hence, codes are usually designed to maximize dfreerather than to minimize BER, and their performance is verified using simulation. The ratio between the free Euclidean distance of a coded system and that of an uncoded system is called the coding gain. Specifically, Coding gain = 20 log,,

)

dfree(coded) dB. d,,,, (uncoded)

If the average energy of the uncoded constellation is increased by the coding gain, the uncoded system will have the same error resistance as the coded system. Comparing coding schemes based on coding gain is useful only if the compared systems have the same rate (bits/dimension), because codes with a higher rate will naturally have a lower dfree.In addition, coding gain is a measure of relative energy efficiency only; the bandwidths of the compared systems must be separately considered.

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

17

1. The Encoder

Codes are designed from the standpoint of adding coding to an uncoded system. For an uncoded system, the number of points in the signal constellation is I U1, but after adding an encoder the signal constellation must have \ Y1 points. Normally, I Y I 2 21 UI (see Section IV.C), so the uncoded constellation must be at least doubled in size. Points can be added to a constellation in two ways. The first way is to concatenate adjacent channel symbols, as in Eq. (1 I), and halve the modulation interval. This effectively increases the dimensionality of the constellation. The second way is to add points to the constellation directly, without increasing the number of dimensions. The former possibility increases the required bandwidth of the transmitted signal, which is unacceptable in a bandlimited environment. The latter choice requires a higher average energy to maintain interpoint distance, since there are more points per dimension. However, the energy efficiency (see Eq. (28)) added by the encoded more than compensates for the loss. Codes that use the latter method of constellation expansion are termedalphabet redundant. All codes add redundancy. With alphabet redundant codes, the redundancy is absorbed by increasing the number of points in the constellation (the channel alphabet), and not by transmitting more channel symbols (Biglieri, 1984). Forward error correction (FEC) alphabet redundant codes are divided into two major types: those with memory, and those without. Memoryless codes, or block codes, act as mapping functions. The input data is divided into sections, and each section is mapped into a larger output section. The inputs and outputs are generally, but not always, binary. Hamming’s rate (7,4) code is a block code where each 4-block of input bits is mapped into a 7-block of output bits. However, Hamming’s rate (7,4) code is atypically small. A popular Reed-Solomon code, for example, has rate (384,240) (Berlekamp et al., 1987). Typically, a rate (384,240) code would not use a constellation with 2284 signal points. Instead, several small constellations with few dimensions would be used sequentially. This is effectively a large multidimensional constellation. Because the component constellations are identical and not optimized for consecutive use, the gains allowed by higher dimensions are usually not realized. Although block codes act as mapping functions, this description is useless when the block size is large. For the rate (384, 240) code, enumerating the mapping function requires a table with 2240 entries. This makes encoding difficult and decoding impossible. Instead, block codes are described using polynomials over a finite field. This reduces the problem of both encoding and

18

HOWARD .I.CHIZECK AND MITCHELL D. TROTT

decoding to the simpler (but far from trivial) problem of finding roots of a finite polynomial (Berlekamp, 1968). Although block codes are frequently used for discrete memoryless channels, we are interested in codes with memory, the so-called “convolutional codes.” Rather than operating on large blocks of input data at once, convolutional codes process small pieces of data incrementally. Thus, the encoder is just a discrete-time discrete-state dynamical system. The most general type of code with memory is the trellis code, whose design and structure are the subject of the next two sections.

111. TRELLISCODES:STRUCTURE In this section we examine properties of trellis codes related to their structure as finite state machines, rather than their specific function as errorcorrecting codes. Section 1II.A gives a precise definition of trellis codes that’s more general than the definitions used by other authors. Trellis diagrams, the primary graphical tool for describing trellis codes, are explained in Section 1II.B. The distinction between finite and infinite memory systems and their relationship to trellis codes is addressed in Section 1II.C. The lack of a careful definition of finite and infinite memory systems has led to some confusion in the literature, which we attempt to resolve here. The related concepts of equivalence and minimality are considered in Section 1II.D. Two forms of equivalence are defined; each is appropriate in a different setting. Again, the lack of a clear definition of equivalence has led to confusion in the literature, especially when rotational invariance is considered. Finally, Section 1II.E addresses catastrophic error propagation, a type of decoder failure related to the structure of the encoder’s inverse. A. Trellis Codes A trellis code is a finite state machine whose outputs select points from a finite constellation of points in n-dimensional Euclidean space. We refer to the finite state machine alone as the encoder, while the combination of the encoder and constellation is the trellis code. Trellis codes were originally defined by Ungerboeck (1982) as linear sequential circuits (see Section 1V.D) followed by a mapping onto a specified constellation. Calderbank and Mazo (1984) expanded this definition to include all discrete-time sequential systems with a finite input memory. Recently, and most generally, trellis codes have been defined as arbitrary finite-state machines (Divsalar et al., 1987; Zhu and Clark, 1987). Despite the

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

I9

change in definition, trellis codes are still called "convolutional codes," "generalized convolutional codes," or even "generalized feedback codes," although as nonlinear systems they have little to do with convolution. Here, a trellis code is defined as a finite state machine described by a constellation C c R P , input, state, and output sets V , S, and Y, functions f : ( U , S )+ Y, y : ( V , S )+ S, and M : Y 4 C such that

zk

(31)

= M(yk),

where uk E U, s k E S, yk E Y, and zk E C for k = 0,1,2,... The function M : Y A C isn't strictly necessary, but the use of distinct constellation and output sets helps separate the structure of the modulator from the notion of trellis codes as abstract systems. The initial state of the system is unspecified because it's unimportant for a minimal encoder (see Section 1II.D). We require more general definitions of f' and g than those implied by Eqs. (29) and (30). Let f : S x U k f ' -+ Y determine the output of the trellis code in response to a length k + 1 input sequence from a particular initial state. That is, for any so € S, { u o , . . .,uk; E U and k 2 0, Y k =J'("s(sO,uO)

,...,Uk-,),

uk-l)?

= f ( s o , U O . . ' uk).

uk)

(32) (33)

Likewise, let y:S x U k + Y determine the state reached by the trellis code in response to a length k input sequence: sk

= ~ ( y ( " ' ~ ( s O ? u O )u>k .- 2. ') ,> u k =g(so, u o " ' u k - I ) .

1)

(34) (35)

Although the above description is time-invariant, periodic or cyclic behavior is possible. The potential utility of such behavior and its relationship to finite group homatons is discussed in Section V.G. B. Trellis Diagrams A trellis diuyram is a graphical tool depicting the state transition and output functions of a trellis code. Trellis diagrams are bulky and inconvenient, especially when IS1 is large. However, they clearly illustrate any symmetries in the state-transition function, and they are useful for heuristically designing small trellis codes.

20

HOWARD J. CHIZECK AND MITCHELL D. TROTT

k

k+ 1

A

B

C

D FIG.6. A simple trellis diagram.

At each time step, the elements of the state set are represented as a vertical column of dots, called nodes. This is shown in Fig. 6 with S = { A , B , C , D } . Because trellis codes are normally time-invariant, only one time step of the trellis is included in a diagram. The state transitions allowed by g(0) are depicted as branches connecting the nodes at time k to the nodes at time k 1. There are I UI branches leaving each node, one for each input element. The example in Fig. 6 has U = (0,l). Two branches connecting the same pair of nodes are called a parallel transition. A trellis with parallel transitions can be found in Fig. 18. Often, a trellis code’s set of reachable output sequences is more important than its input-output behavior (see Section 1II.D).Input labeling is usually omitted from the diagram in such cases. When no labeling is given, by convention the topmost branch leaving a node is assigned the first element of U, the next highest branch is assigned the second element of U, and so on. The trellis in Fig. 6 is consistent with this convention, so the input labeling could be removed without causing ambiguity. The labels indicating the correspondence between nodes and elements of the state set are often omitted as well. Every branch (state transition) in the trellis has a corresponding output element determined by f(.).This correspondence is indicated either by individually labeling the branches using f(-), or by placing labels to the left of each node. In the latter case, the leftmost element corresponds to the topmost branch leaving the node, the rightmost element corresponds to the bottommost branch, and so on. The trellis in Fig. 6 is repeated in Fig. 7 to demonstrate both forms of output labeling, with Y = { A , B, C, D}.

+

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

21

kt I

k

FIG.7. A simple trellis diagram with output labeling only.

TABLE I STATE TRANSITION TABLE FOR FIG.6 Uk =

0

Uk =

1

Sk

Sk+ I

Yk

'k+ I

Yk

A B C D

A C A C

a b

B D B D

d a b

C

d

C

An alternative to a trellis diagram, formed by explicitly specifying the functions f(-) and g(-), is given in Table I. Note that Table I and Fig. 6 do not define a trellis code, because the function M ( - )and the constellation are not specified. A suitably labeled QPSK constellation is shown in Fig. 5. Input data are encoded by following a path through the trellis. For example, with initial state so = A , the path in response to input sequence { u o , u l ,...} = { l , O , l , l ,... } is { s o , s L ,...} = { A , B , C , B , D,...) with corresponding output sequence { y o ,y , , . . .f = {c,b, a , d , . , .), as shown in Fig. 8. C. Finite and Infinite Input Memory Systems

An important aspect of trellis codes unrelated to their error resistance is the distinction between finite and infinite input memory systems. A system has a finite input memory (FIM) if its output can be expressed as a function of a

22

HOWARD J. CHIZECK AND MITCHELL D. TROTT

FIG.8. A path through a trellis.

(fixed) finite number of past inputs. This implies that a constant input must eventually produce a constant output. A system which is not FIM is called an injnite input memory (IIM) system. IIM systems may or may not eventually produce a constant response to a constant input. Infinite input memory systems are sometimes called feedback systems, while finite input memory systems are sometimes identified as feedforward or feedback-free. Formally, a system has a finite input memory if there exists a u 2 0 and a function F : U"" -+ Y such that

for any sk - E S, {uk- ",. . . ,uk) E U,and k 2 v, as in Fig. 9. The minimum such u is called the constraint length of the system. A linear system is FIM if and only if it has a finite impulse response. There is no such test for nonlinear systems because their input sets have no zero element. The structure of IIM encoders is relatively unrestricted. FIM encoders, on the other hand, have a very special structure: There always exists a realization of a finite input memory system where the state transition function g(.) acts as a simple shift register (see Fig. 9). Since g ( - ) is entirely determined by the constraint length u, the behavior of an FIM encoder depends only on f(.) and M(.). This makes FIM encoders easier to enumerate than their IIM counterparts, and it also simplifies many problems of analysis and hardware.

FIG.9. Block diagram of a general finite input memory system.

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

23

Perhaps because of the difficulty in enumerating IIM encoders, and perhaps also because of a mistaken generalization of Forney’s (1970) results for linear sequential circuits to arbitrary trellis codes (see Section IV.D), IIM encoders have been largely ignored. It is possible that there exist IIM trellis codes that marginally outperform the best known FIM codes, but this remains an open question. Regardless of their performance relative to FIM encoders, IIM encoders are important because they are required for rotational invariance (see Section VI). Finite and infinite input memory trellis diagrams can be difficult to distinguish. The following theorem gives a necessary condition for a trellis diagram to be FIM.

Theorem 1. An input-output minimal (see Section 1II.D) finite input memory trellis code depicted in a trellis diagram must have exactly (UI horizontal branches, each labeled with a distinct element of U. Proof: For each of the I UI possible constant input sequences an FIM system must eventually settle to a constant output sequence, which for a minimal system implies a constant state sequence. That is, for each u E U there must exist a single x E S such that x = y(x, u), or equivalently, for each u E U there must exist a single horizontal branch. Necessary and sufficient conditions for a trellis code to be FIM are given in the definition: The output of the code must be determined by a finite number of past inputs. To test a trellis code algorithmically for a finite input memory, select longer and longer input strings and verify that the final output in response to an input string is independent of the initial state. If this holds for all input sequences of length v and not for v - 1, then the trellis is FIM with constraint length v. The algorithm terminates because a system cannot have a finite input memory with u 2 ISI. Examples of FIM and IIM trellis diagrams are given in Fig. 10. In all cases, 1 UI = 2. Figure 10a has three horizontal branches, so by Theorem 1 it must be IIM. The two horizontal branches in Fig. 10b are both labeled with u = 0, so it must also be IIM. Both Fig. 1Oc and Fig. 10d satisfy the conditions of Theorem 1, but only Fig. 1Oc is FIM.

D. Equivalence and Minimality The concepts of equivalence and minimality are of central importance to code design and enumeration. A minimal code is the “smallest” of all equivalent codes; a minimal realization of a code is often the simplest

24

HOWARD J. CHIZECK AND MITCHELL D. TROTT

u=o

(a 10. Finite and infinite input memory trellis diagrams: (a) IIM (three horizontal branches), (b) IIM (two horizontal branches with same label), (c) FIM, (d) IIM (a zero input can cause periodic behavior). FIG.

realization to analyze and construct. Equivalence is important because trellis codes are designed largely by enumeration (see Section 1V.D). For efficient enumeration, only one representative from each set of equivalent codes should be examined. We will introduce two definitions of equivalence: input-output equivalence and ouput equivalence. Using standard algebraic systems theory terminology, two states x and x' are distinguishable if f ( x , u o . u,') # f(x', u o . . . u k )for some {uo,. .. ,Uk} E U. Otherwise, the states are indistinguishable. If all states are distinguishable, the system is obseruable. State x' is reachable from state x if there exists an input sequence that drives the system from x to x', i.e. there exists { u o , . . . ,uk} E U such that g(x, uo...uk)= x'. Mutually reachable states communicate; if all states communicate, the system is controllable. The delay of a system is the maximum 1 such that f ( x , uo u k ) = f ( x , uo u k ) for all x E S, all ui,ui E V , and 0 Ik < 1. Figure 11 shows a delay-1 version of the trellis in Fig. 6 . All systems are at least delay 0. In a coding context, indistinguishable and noncommunicating states are useless. We therefore define a system that is both controllable and observable to be input-output minimal. Observability insures that each encoder state represents different future behavior, while controllability insures that the encoder has no transient states, and that the initial state of the encoder does not affect long-term performance. The irrelevance of initial state is important e

1 . .

+

-

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

25

FIG. I 1. A delay-l version of Fig. 6.

because trellis codes operate on (effectively)one-sided infinite input sequences. Figure 12a shows an input-output minimal trellis, while Figs. 12b- 12e show several minimal and nonminimal realizations of the same. Observe that input-output minimality is highly sensitive to input labeling. Two input-output minimal trellis codes are said to be input-output equivalent if for some choice of initial states they produce identical output sequences in response to identical input sequences. The concept of inputoutput equivalence does not apply cleanly to nonminimal systems, but fortunately only input-output minimal systems are important for coding purposes. Input-output equivalence is not the most general definition of equivalence possible. For example, a trellis decoder (see Section 1V.A) works by finding the most likely path through the trellis based on the received signal points. The input sequence corresponding to that path is then extracted. Since the extraction of the input sequence is independent of the decoding process, the input labels of an individual node in the trellis can be freely permuted without affecting the code’s performance. Similarly, code performance is not affected by transforming the constellation C (or M(.))by any distancepreserving automorphism. The irrelevance of input labeling and several other more subtle types of equivalence can be precisely stated. Two systems with the same set of reachable output sequences are termed output equivalent, where the reachable output sequences of a system are the sequences ( f ( x ,u,),f’(x, u o u l ) ,. . ., f ( x , u,, . . . u k ) }for all x E S , ui E U, and k = 0, I , 2,. . . . Output equivalence is a very general concept. For example, adding a unit delay to the input of a code markedly changes its input-output behavior (see

26

HOWARD J. CHIZECK AND MITCHELL D. TROTT

A

a

C

(4

(4

FIG.12. Input-output minimality. (a) Minimal trellis. (b) Nonminimal; D and E indistinguishable. (c) Input-output minimal; D and E distinguishable. (d) Nonminimal; {A, B, C, D} and {E} do not communicate. (e) Nonminimal; {E} does not communicate with other states.

Fig. 1l), but does not affect the set of reachable output sequences. The input labeling of an FIM system can always be permuted to convert it into an output equivalent IIM system. In fact, Forney (1970)showed that any LSC encoder is output equivalent to a finite input memory LSC. Output-equivalent codes are interchangeable for almost every purpose, with one major exception. As discussed in Section VI, rotational invariance is a function of a code's input-output behavior, not its set of reachable output sequences. Hence, when designing rotationally invariant codes, input-output equivalence is operative, infinite input memory systems are important, and the input labeling on the trellis diagram should always be indicated. This has been neglected by several authors.

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

27

u=o; y=u P

u = l ; y=b

(a) FIG. 13. Output minimality: (a) input-output minimal because all states distinguishable; (b) output minimal realization of (a).

An encoder with as few states as any other output equivalent encoder is termed output minimal. Output minimality is harder to characterize than input-output minimality because the functions f(.) and g ( - ) describe an inherently input-output relationship. Intuitively, an output minimal code is at least controllable, observable, and zero delay. For example, the delay-1 trellis in Fig. 11 is input-output minimal but not output minimal. A more difficult case is shown in Fig. 13. The three-state code in Fig. 13a is inputoutput minimal because all states are distinguishable, but a one-state output minimal realization is shown in Fig. 13b. As output minimality is difficult to characterize, it provides little assistance when applied to trellis codes in general. Its usefulness is more apparent when combined with a structured algebraic class such as LSCs (see Section 1V.D). E . Catastrophic Error Propagation

Catastrophic error propagation is a type of decoding failure related to the structure of the encoder’s inverse system. The encoder’s inverse is used by the decoder to determine the input sequence corresponding to the received channel symbols. Like the encoder, the inverse encoder is a finite state machine with either a finite or an infinite input memory. When the encoder has an IIM inverse, a single channel error can cause an infinite propagation of decoding errors. This type of decoding failure is termed catastrophic error propagation (CEP) (Forney, 1970). A code with an TIM inverse is said to be catastrophic. Catastrophic codes are avoided in practice. The trellis code in Fig. 1Oc is catastrophic. A received sequence {a,a, c, a, a, a,. . . } decodes into { 1,1,0,0,0,0,. . .} while a received sequence {a,a, b,a, a , a . . .} decodes into {O,O, 1, I , I , 1,. . .}. The decoder’s inability to

28

HOWARD J. CHIZECK AND MITCHELL D. TROTT

find the correct initial state allows a single transmission error converting ‘c’ to ‘b’ to cause an infinite number of decoding errors. Define an error eoent as a pair of trellis paths starting at the same state, ending at the same state, and not intersecting at any state between. Some reflection shows that the following statements about an observable trellis code are equivalent: 1. The code is catastrophic. 2. The code has an infinite input memory inverse. 3. The encoder state cannot be determined solely by examining a finite number of encoder outputs. 4. There exist two distinct trellis paths with identical output sequences. 5. There exists an infinitely long error event with a finite Euclidean distance. 6. There exists an infinite number of error events with the same (finite) Euclidean distance. There exist unusual cases where a catastrophic trellis code is not subject to CEP. Consider Fig. lob, which is identical to Fig. 1Oc except for a change in input labeling. The inverse system is still IIM, but now the received sequence {a,a, b, a, a, a, . . .} decodes into (0,0, 1, 0, 0, 0, . . .}, so catastrophic error propagation does not occur. Such behavior is impossible for LSCs and finite group homatons, and point 6 above implies that catastrophic codes perform poorly (see Eq. (26)) whether they are subject to CEP or not. An algebraic test for catastrophic error propagation exists only for linear sequential circuits (Massey and Sain, 1967, 1968); an algorithmic test for an IIM inverse, such as the one given in Section III.C, must be used for all other cases.

IV. DESIGNING TRELLIS CODES In this section we focus on the error-correction and design aspects of trellis codes. This material is largely review. Section 1V.A describes the Viterbi algorithm, a form of maximum likelihood trellis decoding used to correct transmission errors. Section 1V.B gives an example of free Euclidean distance, a common benchmark of trellis code performance. The heuristic code design techniques pioneered by Ungerboeck (1982) are described in Section 1V.C. The primary alternative to heuristic code design is an exhaustive search over a small, well-structured class of algebraic systems. The classes of systems used by previous authors, such as linear sequential circuits, sliding window codes,

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

29

and coset codes, are examined in Section 1V.D. We conclude that a more general algebraic setting is needed to represent many useful codes. A. Viterbi Decoding Trellis codes are usually decoded using a form of dynamic programming known as the Viterbi algorithm. The goal of decoding is to find the most likely trellis path taken by the encoder based on the received signal points. When the received signal points are corrupted by additive white Gaussian noise, the most likely path is the one “closest” to received sequence, with closeness measured by Euclidean distance (see Section 111). The decoder must therefore find the trellis path with the minimum Euclidean distance from the received sequence. An outline of the Viterbi algorithm follows; a thorough tutorial is provided in Forney (1973). At each step the algorithm maintains a suruiuor list. The list has (SI entries-one for each state. The survivor for state x at time k is the most likely encoder path ending at sk = x given observations up to time k . Each survivor has a cumulative distance determined by the survivor’s squared Euclidean distance from the received signal points (see Eq. 24)). The survivor with the minimum cumulative distance (maximum likelihood) is the decoder’s current estimate of the encoder’s path. As time advances and new points are received, the survivor lists are updated based on a standard dynamic programming approach. The algorithm is perhaps best illustrated by example. Example: Consider the trellis diagram showin in Fig. 6. We will assume a simple 4-AM constellation (Fig. 4b) with a H 3, d H 1, c H - 1 and b H - 3. The input data consist of a constant 0-valued sequence, resulting in a constant A-valued state sequence and a constant a-valued output sequence. The constant a output sequence is transmitted as a constant 3 sequence of signal points. Assume that these points are corrupted by noise and received as {3,3,2,1,5,3,3,3,. . .} (using integers simplifies the example). At time k = 0, before receiving Co, the survivor list is empty and the distances are 0, as in Fig. 14a. When the signal point a^, = 3 is received, a modified copy of the encoder’s trellis is appended to the survivor list. Instead of the usual output labeling, the branches of the modified trellis are labeled with their squared Euclidean distance from the received point. That is, the branches leaving state x are labeled with I I M ( f ( x ,.)) - CJ2, as in Fig. 14b. Using the modified trellis and the cumulative distances for each survivor, the minimum distance path to each state at time k + 1 = 1 is found and the survivor list and cumulative likelihoods are updated.

HOWARD J. CHIZECK AND MITCHELL D. TROTT

18“.....

,.,.... .: ..*’ *.. ..

%.

i i

.......

.......................... 2 113-(-3)11=36

.

0,

0,

1,

5-

9,

9,

9-

9-

9-

9-

9-

9,

9,

9,

4

4

5

9

21

13

29

29

21

29

29

29

29

29

(4 FIG.14. Viterbi decoding: (a) initialization, (b) new point 6, = 3 received, (c) new point 6, = 3 received, (d) survivors for first 15 steps.

At time k = 1 the survivors for states A and B are equally likely. The state A survivor has uo = 0, while the state B survivor has uo = 1. When the point = 3 is received, as depicted in Fig. 14c, the above steps repeat. At time k = 2 the survivor for state A is the clear winner, so the decoder estimates that uo = 0 and u 1 = 0. The survivor lists for the next 13 steps are shown in Fig. 14d. At k = 15, the state A survivor is most likely, with a cumulative squared Euclidean distance of 9. The decoder has overcome the transmission errors . Note that the decoder needed 13 time steps before the survivors agreed on the values of so, y o , and u o . A sudden burst of noise at (say) k = 10 might change the decoder’s estimate of uo. Regardless of the received sequence, however, the “tails” of the survivors must eventually agree. This means that the decoder needs only a finite memory of received channel signals. Although finite, the required memory can be quite large: The decoder for our small four-

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

31

state example must remember more than 13 past values, and the memory requirements for larger codes grows rapidly and soon becomes prohibitive. Suboptimal algorithms can reduce the storage problem with only a slight loss in performance (Wilson et al., 1984). rn B. Calculating Free Euclidean Distance

An error occurs in the decoder when an incorrect path becomes more likely than the correct one. Hence, to minimize the probability of error, all paths should be as “far apart” as possible. As discussed in Section ILH, the asymptotic error rate for a code is determined (primarily) by dfree,the Euclidean distance between the closest two paths. Calculating the free Euclidean distance of a code is similar to maximum likelihood decoding. To calculate drree,one must find the closest two encoder paths. For maximum likelihood decoding, one must find the path closest to a fixed sequence. However, determining dfreerequires I S12 dynamic programming states, while Viterbi decoding needs only ISI. Substantial simplifications are possible when the encoder is linear and the constellation is well structured (Zehavi and Wolf, 1987), but for large nonlinear codes (IS1 > 32) the calculation of dfreeis a computationally expensive task. In general, the closest two encoder paths will coincide for k I 0, diverge at k = 0, and remerge sometime later. A dfreepath for the trellis code in Fig. 6 is shown in Fig. 15, assuming a 4-AM constellation with a H 3, d H 1,c H - 1 and b H -3. For this example,

$,,,= ( I ~ c - ~ 1 1 ’ = (42

+ Ild - c1I2 + Ild

-

b112)”2

+ 2 * + 42)”*

(37) (38)

= 6.

(39) a

b (-3) FIG. 15. A free Euclidean distance path for Fig. 6.

32

HOWARD J. CHIZECK AND MITCHELL D. TROTT

Several other paths achieve the same (minimum) Euclidean distance. The average energy of the 4-AM constellation is - 3)’ + (- 1)’ + 1’ + 3’) = 5. For comparison, an uncoded system would transmit the same one bit per symbol using a 2-AM constellation with the same average energy. The free Euclidean distance of an uncoded constellation is the distance between the two closet signal points, which in this case is 2 f i . The coding gain for this trellis code is therefore a modest 20 log1,(6/2fi) = 2.553 dB.

a((

C . Heuristic Code Design As pioneered by Ungerboeck (1982,1987), good trellis codes can often be designed heuristically. The free Euclidean distance of a trellis code is a function of its output labeling, allowed state transitions, and constellation. These factors are surprisingly uncoupled: A “good” constellation will perform well for a variety of trellis codes, and a “good” set of allowed state transitions can be used with many different constellations (Forney et al., 1984). For example, the state transition diagrams in Fig. 16 are optimal (in the sense of maximizing d,,,,) for most symmetric constellations. The number of states IS( in the encoder is determined by the maximum acceptable decoder complexity. Large codes have better dfreevalues than small ones, but they also require more complicated decoders. In addition, larger and larger codes face diminishing returns as their performance approaches channel capacity. We’ll assume that both IS1 and IUI are given as design constraints.

X

FIG. 16. Optimal state transitions for IS1 = 2 , 4 , 8 , 16.

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

33

Diagrams similar to those in Fig. 16 can be generated by following several “rules”: 1. If one branch has parallel transitions, all branches must have parallel transitions. 2. There must be I UI branches entering each node. 3. The trellis must be highly symmetric. 4. If two trellis paths diverge, they must not be able to remerge for several time steps.

Rules 1 and 2 insure that all states in the trellis are visited with equal frequency, while rules 3 and 4 tend to insure that the closest two trellis paths have a large dfree. Selecting the constellation is more difficult. The size of the constellation is usually chosen as ICI = 21UI. The factor of 2 is arbitrary, although Ungerboeck justifies this expansion factor using information theoretic arguments. As a practical matter, this choice works well with binary LSCs (see Section 1V.D). Smaller constellations are generally not useful, but larger constellations may have value. As discussed in Section II.G, the number of dimensions and the location of points in the constellation have an important effect on code performance. However, bandwidth constraints, limited peak energy, and other hardware concerns often dictate constellation design. For a thorough presentation of recent advances in multidimensional constellation design, see Forney (1988). The final step in heuristic code design is the labeling of the branches of the trellis diagram with points from the constellation. Ungerboeck’s technique of mapping by set partitioning is the simplest method; more sophisticated variations have been recently suggested (Calderbank and Sloane, 1987; Forney, 1988). The key to this technique is to partition the constellation into subsets of increasing interpoint distance, as in Fig. 17. Because the two paths that determine dfreemust at some stage diverge and later merge, we can insure a good dfreeby labeling the branches leaving each node with points from just one subset, i.e. {a,c} or {b,d}. If we do the same for the branches entering

-I

-b 3

K1

-3

FIG. 17. The partitioning of 4-AM.

d

I

-

I

34

1 I

1

-

HOWARD J. CHIZECK AND MITCHELL D. TROTT

(0.11

binary inputs (0,l)

“,b,c,dl

mapper

mapper

c

;to

$lol

;If

$11

U (b)

FIG. 18. Parallel transitions and partial uncoded modulation: (a) partial uncoded modulation; (b) a realization of (a) using parallel transitions; (c) 16-QASK labeled for use with either (a) or (b).

each node, a dfreeof at least (42+ 42)(1/2) = 4fi is guaranteed. The trellis in Fig. 6 was designed using this method. Mapping by set partitioning works best when IS1 is small (IS1 < 32). A simple method of extending set partitioning to trellis codes with large I UI and IC1 is to use partial uncoded modulation. In this method, the output of the encoder selects a “coset” of the constellation rather than an individual point. Several uncoded bits bypass the encoder to choose a point from the selected coset. In effect, the uncoded bits act as parallel transitions in the trellis diagram. Figure 18 shows two equivalent representations of the same code: one with parallel transitions, and one without. Codes with very large constellations can be built with this method. The coding gains of heuristically designed codes range from 3 dB for fourstate codes to over 6 dB for codes with 256 states. Currently, the best known codes are about 1-2 dB better (Forney, 1988). Information theoretic arguments show that further improvements are likely to be small. Despite their usefulness, heuristic methods are ineffective for designing very large codes or rotationally invariant codes (see Section VI). For such cases, or when small improvements are important, a different approach is needed.

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

35

D. Code Design by Enumeration The primary alternative to heuristic design is an exhaustive search. Since there is no known direct way to build a code with a given dfree,when heuristics are inadequate trellis codes must be designed by brute-force search over some specified class. Each code in the class is individually constructed and assigned a performance measure, and the best codes are retained. It’s not possible to search the class consisting of all codes with a certain IS(, IU(,and prespecified constellation. Even when IS( is small, the size of this class is astronomical. Moreover, the members of this class are not easy to generate. There is no simple procedure, for example, that lists all 8-state trellis codes. One way to improve searching efficiency is to formulate simple rejection criteria that weed out “useless” codes, such as those that are not invertible. But these kinds of tests are difficult to formulate for arbitrary trellis codes. Another approach is to immediately reject codes that are equivalent to ones already considered (see Section IILD), or, even better, to only test a single representative from each set of equivalent codes. Again, it is difficult to determine a priori if two arbitrary trellis codes are equivalent, and the computations involved in finding a representative code from each equivalence class are prohibitive. The problem of enumeration can be partially resolved by defining codes as members of a class of structured algebraic systems. In a mathematically structured setting, equivalence classes can be created and pretests formulated; codes can be described in a way suitable for enumeration. An ideal structured class would allow the direct construction of codes with desirable properties, eliminating enumeration entirely. The price of structure is the loss of generality, as many codes may be excluded because they don’t lie in the specified class. The challenge is to find a mathematical setting with enough structure for analysis, yet with enough generality to encompass a wide range of useful codes. Many settings have been used in the past. Ungerboeck’s (1982) trellis codes consist of a binary linear sequential circuit followed by a mapping of coded bits into channel symbols. Calderbank and Mazo (1984) consider the larger class of trellis codes whose output is a function of a sliding window on the input data stream. The coset codes of Calderbank and Sloane (1987)consist of a “generalized” convolutional code whose outputs are cosets of a n-dimensional sublattice of signal points. These approaches are considered next. A linear sequential circuit (LSC), or convolutional code (Massey and Sain, 1968) is a discrete-time sequential system over a finite field K with state sk E K”,

36 input

HOWARD J. CHIZECK AND MITCHELL D. TROTT uk E

K", and output y k

E

K' such that

Sk+ 1 = A S , yk =c s k

+ BU, +

DUk,

(40) (41)

where A , B, C , and D are constant K-valued matrices of the appropriate dimension. An LSC alone is not a trellis code; the addition of a constellation C and a function M : K ' + C that maps encoder outputs to signal points completes the description. LSCs are the most structured and analytically rich class of algebraic system used to represent trellis codes. Their structure allows the derivation of powerful results, including Massey and Sain's (1967, 1968) inverse construction and catastrophic error propagation conditions, Forney's (1970) canonical class of LSC encoders, and many others. Forney showed that any infinite input memory LSC encoder can be replaced by an equivalent finite input memory LSC. Specifically, any LSC is output equivalent (see Section 1II.D) to a minimal FIM LSC with a 0-delay FIM inverse. Finite input memory LSCs are easy to enumerate, even for relatively large values of IS[.The choice of M(.)and C is usually made prior to an enumerative search. Despite their benefits, LSCs have several significant limitations. LSCs are said to be linear because when starting from the zero (identity) state, if input sequence { u k } produces an output sequence { y k } , and { u k } produces { z k } , then {uk + U k } must produce { y , + z k } . This artificial constraint on the input set makes LSCs sensitive to changes in input labeling; rearranging the input labels for a single state can change an LSC to a non-LSC. When output equivalence is operative (see Section 1II.D) this sensitivity is beneficial because many equivalent codes are automatically excluded. However, when input-output equivalence is important (as for rotationally invariant codes), the utility of LSCs is diminished. Another limitation of LSCs springs from the requirement that K be a field. The cardinality of a field is always a power of a prime number (Fraleigh, 1982). Hence, if the input set is binary, the cardinality of the state and output sets must be a power of two. This constraint is not too serious, because codes with state cardinalities of 4, 8, 16, 32,. . . perform quite well and are easily realized using digital hardware. However, a code with 24 states and a 36-point constellation can never be realized as an LSC. Trellis codes with unusual sizes, although unlikely to produce great performance gains, may allow more finely tuned tradeoffs between complexity and performance. Calderbank and Mazo (1984) define trellis codes as arbitrary finite input memory systems (see Fig. 9) with binary inputs and one- or two-dimensional constellations. Their approach is unique in that the constellation mapping function M(.)is absorbed into the output function f(.). This allows an

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

37

enumerative search to consider both .f(.)and M ( - ) simultaneously. Several new codes have been found using this method, as have upper bounds on code performance (Calderbank et al., 1985). The most significant limitations of sliding window codes are their restriction to binary-valued inputs and their inability to represent any encoders with infinite input memory. Coset codes, as defined by Calderbank and Sloane (1987), are a generalization of finite input memory LSCs that operate over rings rather than fields. The encoder outputs are cosets of a lattice of signal points, with several uncoded bits selecting a particular point from the chosen coset. As with FIM LSCs, coset codes can be efficiently enumerated. Unlike LSCs, coset codes are not restricted to power-of-two input, output, and state cardinalities. The central feature of coset codes is the geometric relationship between the encoder output set and the constellation; coset codes provide an alternative to Ungerboeck’s (1982) technique of “mapping by set partitioning.” Powerful trellis codes have been found using coset methods (Calderbank and Sloane, 1987; Forney, 1988), establishing the value of using more general algebraic settings than LSCs. As with sliding window codes, coset codes are limited by their inability to represent infinite input memory systems. The class of algebraic systems introduced in the next section addresses this and other limitations.

V. FINITEGROUPHOMATONS In this section we describe theoretical results for a class of algebraic systems known as finite group homatons (FGHs). Through these results we address two questions: What types of behavior are exhibited by finite group homatons, and assuming that the class of finite group homatons contains useful trellis codes, how do we find them? To search the class of FGHs for good trellis codes we need a description of FGHs suitable for enumeration. This description must be in some sense “efficient”; in particular, each of the infinitely many equivalent realizations of an FGH must have the same description. Section V.B contains results about weighting patterns, a type of input-output FGH description that has this important property. FGHs are more general than linear systems. For example, the zero (identity) state of a linear system has certain unique properties, but there is no such special state for FGHs. In Section V.C we express this notion more precisely. As nonlinear systems, FGHs can exhibit unusual behavior for a few starting steps. Such behavior is related to questions about minimality, and to

38

HOWARD J. CHIZECK AND MITCHELL D. TROTT

the problem of counting the number of reachable states in an FGH trellis code. In Section V.D we discuss FGH minimality and establish new results that show how to eliminate transient behavior when searching for FGH trellis codes. For a trellis code to be useful it must be invertible. That is, it must be possible to infer the code’s inputs by examining its outputs. In Section V.E we review FGH inverse results: There is a simple way to test if an FGH is L-delay invertible, and there is a general inverse construction. The distinction between finite and infinite input memory systems is often blurred when applied to convolutional codes. In Section V.F we show how to identify finite and infinite input memory FGHs. All rotationally invariant FGHs have an infinite input memory (see Section VI). Finally, in Section V.G we explore the kinds of systems that can be modeled as FGHs. We review a theorem that determines when a given system can be realized as an FGH, and give an example of an existing trellis code that is not an FGH. A. Finite Group Homatons

As defined by Karpen and Chizeck (1987), a finite group hornaton (FGH) is a discrete-time sequential system with a finite input set U, a finite state group S = ( S , *), a finite output group Y = (Y,*), mappings b: U + S, d : U -+ Y, and homomorphisms a :S + S , c :S --* Y such that

where U k E u,sk E s, and yk€ Y for k = 0, 1,2,.... FGHs are a generalization of finite group homomorphic sequential systems (FGHSSs) (Brockett and Willsky, 1972; Chizeck, 1978). The input set U of an FGHSS is actually a group, and the b and d mappings are homomorphisms. An FGHSS is similar to a coset code (see Section 1V.D)with a feedback term. The added structure of FGHSSs makes them easier to analyze than FGHs, but sharply restricts the kinds of trellis codes they can represent. FGHSSs are a generalization of linear sequential circuits. Unlike LSCs, FGHSSs are “linear” (see Section 1V.D) only if the output group is abelian. The question of linearity is not meaningful for FGHs because the input set U has no binary operation. Also, for every FGHSS in the identity state an allzero input sequence must produce an all-zero output sequence. FGHs do not have this property because they do not necessarily have a “zero” element in their input set.

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

39

Any LSC has an immediate realization as an FGH. The set K"' is finite, K " and K r are finite groups under addition, and the linear maps A and C are group homomorphisms. Consequently, an LSC can be transformed into an FGH by discarding both scalar multiplication and the linear structure of U , B, and D.Notice that a multiple-input, multiple-output LSC becomes a singleinput, single-output FGH; the multiple inputs and outputs are merged using the direct product structure of groups. The following example demonstrates the immediate realization of an LSC as an FGH. Example: Ungerboeck's eight-state 8-PSK rate scribed as an LSC in the Galois field GF[2]:

trellis code can be de-

(44)

(45)

where sk = [ S , k S l k S O k l T , u k = [Ulkfd()k]T, yk = [y2ky,ky,klT. The output yk is mapped to the constellation in Fig. 19. An equivalent FGH realization is

u = (Z,

x Z,)

s = (Z,

x

Y = (Z, x

01 1

z, x z,, + ) z, x z,, + )

t

010

.001

FIG.19. 8-PSK constellation.

B. Weighting Patterns The performance of a trellis code is determined by its input-output behavior, not by the particular realization that achieves this behavior. Accordingly, LSCs are not usually described using the state-space realization given in Eqs. (40)and (41). A description with no direct reference to state, such as generator polynomials, is used instead. Example: A generator polynomial (D-transform) specification of Ungerboeck's eight-state code (see Eqs. (44) and (45)) is D

1

Y(D) = 1 D2 O

D

where x(D) = C?",x,D-~. FGHs also have a stateless description. A weighting pattern is an infinite sequence of mappings {Dl To,T,, . . .: U + Y } that uniquely characterizes the input-output behavior of an FGH. Given a weighting pattern, the output yk of the corresponding FGH is determined by the past inputs {uo, ulr.. , ,Uk}: Yo = D(U0)

yk

= D(uk)'

(47) TO(#,-1)' T1(uk-2)'"''

Tk-l(uO)'

(48)

The weighting pattern of an FGH with initial state so = x is given by D(.) = d ( * ) c(x),

T ( - )= c(a'(x-' * b(.) * a(x))),

(49) i = 0,1,2,. . .

(50)

where we define a' to be i successive compositions of 'a' with itself, and u0 to be the identity homomorphism. Because the state group is finite, the sequence {a'(.)} is periodic, and so is the sequence { T(.)}.

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

41

Using the abbreviated notation U&,k = ( U l k , UOk) and y 2 k y l k y O k = yok), the weighting pattern generated from the zero state of Ungerboeck's 8-state code (see Eqs. (44)-(46)) is Example:

(y2k,ylk,

= (000,000,000,000,.. .}

D(O0) = 000,

{ '&(OO)}

D(O1) = 100,

{ 7;(01)} = {001,010,000,000,.. .}

D(10)=010,

{'&(lo)}= (100,000,000,000,...}

D(l1) = 110,

('&(ll)}= (101,010,000,000,... }.

Several simple results follow from Eqs. (47)-(50). If a weighting pattern is generated from initial state so = x , then the output Y k in response to the input sequence { u o ,ul,. . . ,u k } from some other initial state x' is yk = D(uk)

T O ( U k - 1)

"

'

T - ~ ( U O ) C(ak(X-' * x')).

(51)

If there exists an input sequence ( w o , , . . ,w j } that drives the FGH from state x to x', then the output y , is also given by yk

= D(uk)

TO(uk-1)

."

T-l(uo)

G(wj)

'*.

T+j(wo),

(52)

implying that c(ak(x-'

* x')) = T ( W j ) ...

(53)

T+j(WO)

for k = 0 , 1 , 2 .... Equations (49) and (50)establish that every FGH has a weighting pattern. Conversely, any periodic weighting pattern can be used to construct an FGH. Define the period and periodic delay of a weighting pattern as the smallest r and t such that q(.)= q+r(.)for all i 2 t. This is shown in Fig. 20. For convenience, let n = t r. One possible FGH realization with so = e (the identity), as modified from Karpen and Chizeck (1987), is:

+

a : Y"

b :U

-+

-+

c: Y " -+

Y",

( x o , x , , . . * , x,-

1) H ( X I , x 2 , .

. ., X , - ~ , X , -

1,x,)

(54)

Y",

u H (To(u), . . . , T,- l(u))

(55)

Y,

(xo,.. . , X n -

(56)

d : U -+ Y,

H xo

u H D(u).

FIG.20: The periodicity of FGH weighting patterns.

(57)

42

HOWARD J. CHIZECK AND MITCHELL D. TROTT

We call this the standard observable (SO)realization of a weighting pattern: It’s analogous to the standard observable realization of a linear system. We construct SO-realizations from weighting patterns in Section VII when searching for new codes, and we also use the SO-realization in proofs. C . Initial State

Notice that the initial state of the SO-realization is always the identity, even if a nonidentity initial state was used in Eqs. (49) and (50) to generate the weighting pattern. The following theorem generalizes this idea. Theorem 2. An FGH with initial state so = x can be transformed into an input-output equivalent FGH with initial states, = e. The transformation is given by the following equations: a*(s) = a(s)

b*(u) = x-’

* b(u) * a(x)

C*(S) = c(s)

d*(U) =

d ( u ) c(x)

(59) (60) (61)

Proof) Application of Eqs. (49) and (50) verifies that the original and transformed systems have the same weighting patterns. They must therefore have the same input-output behavior. Note that each state s in the original F G H is transformed into state x - ’ * s in the new FGH.

Theorem 2 shows that the identity state of an F G H has no special properties; any state can be transformed into the identity via Eqs. (58)-(61). This allows us to assume that the initial state is the identity element when we enumerate FGH trellis codes in Section VII. In contrast, an LSC in the zero state is “unexcited”: A zero input will always produce a zero output and the system will remain in the zero state. For LSCs, however, the concept of initial state can be entirely avoided by using minimal realizations and by considering two-sided rather than one-sided infinite input sequences (Forney, 1970). D. Minimality and Transient States

Given an FGH weighting pattern, it’s useful to know how many states the corresponding trellis code will have. The usual way to determine the number of states in a trellis code is to find a unique minimal realization, one where all states are distinguishable and all states communicate (see Section 1II.D).

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

43

Theorem 3. The SO-realization is observable.

Proof: Given any two distinct states x = (x,,, . . . ,x,- , ) a n d z = (zo,. , . ,z, ,), there must exist a j such that x j # zj, Iterating the definitions of a(-) and c(.) from Eqs. (54)-(57) reveals that c(u’(x)) = x j and c(aJ(z))= zj. It follows from Eq. (51) and x and z are distinguishable at time k = j . When not concerned with rotational invariance (see Section VI), LSCs have a canonical minimal realization (Forney, 1970).Unfortunately, FGHs do not. Deleting noncommunicating and indistinguishable states may result in a structure that isn’t an FGH. Although nonminimal, the SO-realization is observable; a brute-force method of determining the size of an FGH trellis code is to iterate the SO-realization to find all reachable states. This is the procedure used in Section VII. Of course, a trellis code can always be realized as a minimal finite state machine in hardware. But there are problems with this method of determining the size of an FGH trellis code. What if the SO-realization has two or more disjoint collections of communicating states: Which should be kept and which discarded? And what if the initial state of the SO-realization is transient? A state x is transient if there is a state reachable from x that doesn’t communicate with x, making it possible for the system to leave x and not be able to return. Since trellis codes operate on effectively independent uniformly distributed semi-infinite input sequences, transient states increase the complexity of a trellis code without affecting performance. Figure 21 demonstrates several types of transient behavior. In Fig. 21a, state 1 is transient. Although the encoder need never leave state 1, if it does

:g ig

4

4 5

5

(a)

(b)

(c)

(4

FIG.21. Several types of FGH transient behavior: (a) State 1 is transient; (b) states 1 and 2 are transient for at most two time steps; (c) state 3 is transient for only one time step; (d) states 4 and 5 are transient.

44

HOWARD J. CHIZECK AND MITCHELL D. TROTT

leave it will never return. In Fig. 21b, states 1 and 2 are transient, but the encoder can stay in each transient state for at most one time step. The transient state 3 in Fig. 21c is always exited after one time step, but in Fig. 21d the system can alternate between the transient states 4 and 5 indefinitely. In Figs. 21c and 21d, the inputs during the transient period have a lasting effect on future behavior. If an FGH has transient states they will always be of the type depicted in Fig. 21b, as stated in the following theorem. Theorem 4. Regardless of the initial state and input sequence, a given FGH cannot be in a transient state after a certain finite amount of time t’ (defined in Eq. (64)).Moreover, the set of communicating states reached at time t ’ depends only on the initial state, not on the input sequence. Pro08 We will first prove the result for observable FGHs. Choose any initial state so E S and generate a weighting pattern from so using Eqs. (49) and (50). Let l(u) = min{k I T,(o) = T+*(u) t

for all

i 2 k)

= max I(u)

(63)

VOU

t’

(62)

= min I(u) veL1

u‘ = argmin l(u). VE

U

Equation (63) is merely a restatement of the earlier definition of the periodic delay t . Define T’ to be the set of states reachable from so after exactly t’ time steps, and let T be the set of states reachable from so after t’ or more time steps. Clearly, T’ c T. It will sufficeto show that every state in T’ is reachable from every state in T. Assume we are in some state x E T, and that we wish to reach state x’ E T‘. Let { b,, . . . ,b, - I } be an input sequence that drives the system from so to x, and let {a,, . . .,a,. - be an input sequence that drives the system from so to x’. The definitions of T and T’ guarantee that both sequences exist. The input sequence composed of I Y Ir copies of { b, ,. . .,6 , - I Y I r copies of u‘ and one copy of {a,, . . . ,at,- 1}, will take the system from state so to x and then to x’: { u o , ... 9 u r ( y l ( k + I ) + ( , -

t} =

{b,,. . .,b k - l , . . , ,b,, . . . ,b,-

u’, . . . ,u’ a,,

. . . ,at,-

(66)

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

45

The r-step periodicity of the weighting pattern, combined with Eq. (48) and the relation ylyl = e for all y E Y, can be used to show that the effects of all but the final t’ inputs cancel. The state reached by this input sequence is therefore indistinguishable from the state reached by the input sequence { u o , . . . ,CJ,. l}. The FGH is observable by assumption, hence the state reached by Eq. (66) must be x‘ as claimed. For unobservable FGHs, the output group and c homomorphism can always be “extended” to make the FGH observable. One way to make an FGH observable without affecting transient behavior is to concatenate the state group to the output group and force the current state to appear in the output. The theorem then applies to this new observable system. Since the original and extended systems have the same transient behavior, the proof is complete. Note that t‘ in Eq. (64) must be determined from the extended FGH, not the original. rn Theorem 4 guarantees that a state will not be transient if the weighting pattern it generates has t‘ = O(see Eq. (64)).However, a nontransient state may or may not have t’ = 0. Fortunately, the next theorem allows us to discard FGH weighting patterns that have t’ > 0 without losing any codes. Theorem 5. Every FGH has a state that generates a weighting pattern with t ’ = 0. Proof We prove this by construction. Given an arbitrary FGH and initial state, use Eq. (50) to form a weighting pattern. We know from Theorem 4 that FGH transient behavior has finite duration, so we can iterate the system until the transients are past. Pick any u E U, and apply inputs u, = u for i = 0, 1, . . . ,t . The system is now in some nontransient state s,. Generate a new weighting pattern from s,, using Eqs. (50) and (53): D*(.)

=

D(.) T,(u) T,(u) . . . 7;- 1 ( ~ ) ,

T,*(.)= (7;(u).....

(7;+ 1

w

T+,-&]))-l

...

(67)

7;(.)

T + do)).

(68)

Straightforward computation shows that T:(u) = T,+,(u), implying that the new weighting pattern has t*‘ = 0. rn Exumple: This example illustrates the roles of l(u), t, t’, and u‘ in Theorem 4. Let U = ( u 1 , u 2 , u , } , and Y = (0,1,2}. Consider the weighting pattern

D(ul) = 0,

{ 7 ; ( ~ , )= $ (O,O, 1,0,0,0,0,0,0,.. .$;

D ( u , ) = 1,

( 7 ; ( u 2 ) } = { 1,2, l,O, 1,0,1,0,1,. . .};

D(v3)=2,

( 7 ; ( u 3 ) } =(2,0,1,2,0,1,2,0,1, ... }.

46

HOWARD J. CHIZECK AND MITCHELL D. TROTT

For this weighting pattern, r = 6, l(u,) = 3, 1(u2) = 2, and l(u3) = 0. Hence = 0. The system will not exhibit transient behavior.

t = 3, v' = v3, and t'

We have shown how to describe FGHs using weighting patterns, and how to choose weighting patterns to avoid transient behavior. We now show how to construct FGHs that are guaranteed to be invertible.

E . Inverse Systems

Intuitively, a system is invertible if we can always deduce its inputs from its outputs. Clearly, any useful trellis code must be invertible. For a system to be L-delay invertible it must be possible to determine the input uiby examining all outputs up to Y,~+~. Accordingly, the cascade of a system and its L-delay inverse acts as a pure delay of L time units. Any FGH weighting pattern can be tested for invertibility using the following theorem from Karpen (1986), comparable to Massey and Sain's (1 968) invertibility test for LSCs. Define M k : U k +-+' Y k + ' as

Proof: Proven for FGHSSs by Brockett and Willsky (1972), Willsky (1973, 1975) and Chizeck (1978), and for FGHs by Karpen (1986). Corollary 7. An FGH is O-delay invertible if and only if IIm{d(.)}l = I UI.

Forney (1970) showed that convolutional codes with inverse delay L > 0 are uniformly inferior to codes with inverse delay L = 0, but this may not be true for FGH trellis codes, especially when the number of states is large. Corollary 7 implies that each node in the trellis diagram of an FGH with inverse delay L > 0 must have at least two branches with identical output labels. This violates one of Ungerboeck's heuristic design principles: Branches

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

47

emanating from the same node should be labeled with distinct elements of the constellation (see Section 1V.C).But design heuristics may not apply to large trellis codes with long minimum distances error events, leaving the importance of FGH codes with L > 0 unresolved. Given an L-delay invertible FGH, and L-delay inverse system can always be built using the following construction (Karpen, 1986), analogous to the inverse construction for FGHSSs (Chizeck, 1976): Theorem 8. Define a mapping KL: Y -+ U such that KL( y o , . . . ,y L ) = u if ML(u,u o . " u L - = ( y o , .. . ,y L )for some u, uo,. . . ,uL- E U. Otherwise, assign KL(y0,.. . ,y L )any arbitrarily chosen u E U. Using this mapping, the L -delay inverse system is +

uk = sk

+1

KL(yk c(s;l

= b(Uk)

)?

Yk+ 1

c(a(s;')),. . . yk t L C(aL(sk'1)) 9

* a(sk).

(71) (72)

Although the inverse of an LSC is always an LSC, the inverse of an FGH is not always an FGH because KL need not be a homomorphism.

F. Catastrophic Codes and Injinite Input Memory Systems

Catastrophic error propagation is a topic closely related to the construction of inverse systems. Recall that a trellis code is catastrophic if its inverse system has an infinite input memory (see Section 1II.E). Catastrophic trellis codes are undesirable because they allow a single channel error to propagate into a potentially infinite number of decoding errors. Forney showed that every LSC is equivalent (in a certain sense) to a finite input memory LSC with a finite input memory inverse. This may not be true for trellis codes in general, and it is certainly not true when rotational invariance is considered, as can be seen in Section VI. Although it is fairly simple to check an arbitrary trellis for an FIM inverse using a recursive algorithm, a structural check such as the one found by Massey and Sain (1967, 1968)for LSCs is not known for FGHs. As with LSCs, finite input memory FGHs are easier to enumerate than their IIM counterparts. The following result substantially reduces the set of weighting patterns that need to be considered when searching for FIM FGH codes. Theorem 9. An FGH in state x E S has a finite input memory if and only if the weighting pattern generated from x has T(.) = e for i 2 t .

48

HOWARD J. CHIZECK AND MITCHELL D. TROTT

Proofi Sufficiency is obvious from Eq. (48). To show necessity, assume that the input sequence { u k } is constant for all k 2 0. Using Eq. (48) and the definition of the periodic delay t, the output sequence { y k } can only settle to a constant value if TJ.) = e for i 2 t. The SO-realization is unnecessarily large for a finite input memory FGH because the last element of the state vector is always e . Deleting this element results in a slightly smaller realization:

a: Y'

+

Y',

b: U + Y', c:

Y ' + Y,

d : U + Y,

(xo,. . . , x t -

u

1) H

H (To(u),.. .,

(xl,.. . ,x,_ e)

T-l(u))

(xo,...)X t - 1 ) H xo u H D(u).

Note that the a homomorphism now acts as a simple shift register. G. Realizability

FGHs are more general than LSCs. But what kinds of behavior can an FGH have that an LSC can't? And how do we decide if a particular trellis code is really an FGH in disguise? The first result of this section is a method for determining when an arbitrary trellis code can be realized as an FGH.

Theorem 10. An input-output function f ( x , . ) of a trellis code can be realized as an FGH if and only if there exists a group (Y, ). with Im{f(x, .)} c Y such that f ( x ,00 ' ukf ( x , U U O " ' u k - 1) = f ( x , w g ' ' ' wk f(x, UWO ' ' ' wk - 1) "

(73) for all u, uir wi E U and k 2 1. If a trellis code satisfies Eq. (73) then its FGH weighting pattern is D(u) = f ( x , 4

q ( u ) = f ( x ,UO

(74) ' ''

Vk)-'

f ( x , uuo' ' ' u k )

(75)

for any uiE U. Proof: As in Karpen (1986), somewhat simplified because trellis codes always have a finite number of states.

To apply Theorem 10 one must pick an output group Y and a state x. The choice of x is irrelevant: If one state of a trellis code satisfies the theorem, then

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

49

all states will. The choice of Y, however, is more difficult. There is no obvious way to decide how many elements Y should have, or how Y’s binary operation should be defined. One sure way to select Y is to use the free group generated by the elements of Im{f(x,.)}, constrained by the finite set of relations determined from Eq. (73).Coset enumeration (Gardiner, 1986)can be used to produce the output group Y after a finite amount of computation. If the outputs of the original trellis code do not correspond to distinct elements in Y, then the trellis cannot be realized as an FGH. Although coset enumeration can produce infinite groups, it can be shown that any FGH realized with an infinite abelian group can also be realized with a finite abelian group. This may not be true for non-abelian groups. In general, we have observed that the relations generated from Eq. (73) result in groups that are too small rather than too large. Once Y is selected it’s often simplest to assume that Eq. (73) is satisfied and immediately generate a weighting pattern from Eqs. (74) and (75). The SOrealization of this weighting pattern can then be easily verified against the original system. As we will see in the next example, Eq. (73) is useful mainly when demonstrating that a trellis code is not an FGH. Exumple: We will use Theorem 10 to show that Oerder’s (1985) six-state trellis code, depicted in Fig. 22, cannot be realized as an FGH. From Eq. (73), the following equalities must hold for the code to be realizable as

FIG.22. Oerder’s six-state trellis code

50

HOWARD J. CHIZECK AND MITCHELL D. TROTT

an FGH:

..

f(u,00)-' mf(a, 100) = f(a,Ol)-' o f ( a , 101) = f(a, 10)-1 = f ( a , 11)-'

(76)

f(a, 110)

(77)

f(a, 1 1 1).

(78)

The values of f ( a , . ) are found by tracing a path through the trellis. Substituting these values into Eqs. (76)-(78) yields: (O)-l

. . 3

= (2)-1

1

= (3)-1

1

= (1)-1.3,

implying that 2 = 3 and 0 = 1. The elements of Y must be distinct, hence the rn trellis cannot be realized as an FGH.

A positive example of Theorem 10 is given in Section VI when we show that Wei's eight-state 32-CR four-way rotationally invariant code is an FGH. FGHs can realize a much broader class of trellis codes than LSCs. For example, all LSCs must have a transition from sk = e to sk+ = e, but FGHs do not. Indeed, an FGH need not have any state x such that sk = x, s k + = x is an allowed transition. This allows periodic behavior. For example, the state of an FGH can alternate between disjoint subgroups every other time step. Although this property is potentially useful for channels that cannot accept consecutive repetitions of the same symbol, it does not appear to be useful for Gaussian-noise channels. The next result shows how to choose weighting patterns to avoid periodic behavior. Theorem 11. An observable FGH in state x E Swill remain in that state after application of input u E U if and only if the weighting pattern generated from x has 7]:(u)= e for i 2 0. Furthermore, any such x cannot be transient. Proot If u doesn't change the current state, it follows from Eq. (42) that b(u) * a ( x ) = x. Substitution into Eq. (50) shows that T(u)= e for i 2 0. The converse follows immediately from Eq. (48)and the definition of observability. We can now calculate from Eqs. (62) and (64) that I(u) = 0 and t' = 0. Since t' = 0, Theorem 4 guarantees that x is not transient. rn All FGH codes considered in Section VII satisfy Theorem 11. All finite input memory FGHs do too, according to the next theorem. Corollary 12. Any finite input memory FGH has a state x that generates a weighting pattern with T(u)= e for some u E U and all i 2 0.

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

51

Proof Because a constant input must eventually produce a constant output for FIM systems, the trellis diagram of any finite input memory FGH has exactly 1 II( transitions that satisfy Theorem 11. We now have enough tools to search the class of FGHs for trellis codes. We know that every FGH has a weighting pattern and every weighting pattern has an FGH. Weighting patterns fully characterize the input-output behavior of FGHs. The SO-realization is observable, providing a crude way to determine the number of states in an FGH trellis code. Transients are easy to avoid, and invertibility is easy to guarantee. We use these results first in Section VI to derive a method of constructing rotationally invariant FGHs, and then in Section VII to search for new codes.

INVARIANCE VI. ROTATIONAL

The usefulness of many trellis codes is limited by their sensitivity to “phase jumps,’’ a common type of non-Gaussian channel noise caused by inaccurate carrier-phase tracking. The most effective way to reduce phase-jump sensitivity is through specially designed rotationally invariant trellis codes. Rotational invariance is a property of a code’s input-output structure, while a code’s sensitivity to Gaussian noise is determined solely by its set of valid output sequences. Consequently, existing tools used to find codes with good free Euclidean distance are not effective at finding codes that are rotationally invariant. The search for new rotationally invariant trellis codes is hampered by the lack of a unified setting for their analysis and enumeration (Zhu and Clark, 1987). Finite group homatons may provide the needed setting. Not only can FGHs easily capture the symmetries required for rotational invariance, but the results of Section V are well suited to the analysis of input-output behavior. In this section, using FGHs, we derive necessary and sufficient conditions for nondifferentially encoded rotational invariance that can be directly applied to the design of new codes. Our results are derived for twodimensional constellations, but only because there appears to be no clear definition of multidimensional rotational invariance in the literature. Section V1.A gives a simplified explanation of carrier-phase tracking and provides a description of the effects of tracking errors. Section V1.B mathematically defines rotational invariance and its requirements. Certain types of rotationally invariant trellis codes require differential encoding, a process detailed in Section V1.C. The use of differential encoding is not required, however. FGHs are used in Section V1.D to derive easily applied necessary

52

HOWARD J. CHIZECK AND MITCHELL D. TROTT

and sufficient conditions for rotational invariance without differential encoding. Several important rotationally invariant codes are realized as FGHs to demonstrate the power of the new representation. A. Carrier Phase Tracking and Synchronization

In a typical trellis-coded modulation scheme, the modulator and demodulator operate independently; they have no absolute time base. However, the demodulator requires an accurate time base to determine the start of each modulation interval. A timing error at the demodulator appears as a “rotation” in the received signal constellation. To illustrate the effects of inaccurate timing, assume that the clocks of the transmitter and receiver differ by At, and that A t is small compared to the modulation interval. Assume further that the modulator uses 4-PSK, and that the channel is noiseless. Then, during each modulation interval, the correspondence between received and transmitted signals is given by Table I1 (ignoring T k I t < T k + At). The factor o A t is called the phase ofSset and is usually represented as a time varying function d(t). Figure 23 shows the effect of phase offset pictorially. Relative to the transmitted constellation, the received constellation is rotated about the origin by d ( t ) radians. Note that additive white Gaussian noise acts independently of phase offset; if the offset is removed, a code’s performance is still determined by its free Euclidean distance. As in the majority of the available literature, we restrict our consideration here to two-dimensional constellations. Because d(t) drifts slowly in most applications, it can be canceled by adaptive phase-tracking algorithms (Ungerboeck, 1982). After sudden bursts of noise, however, these algorithms may fail. Carrier-phase synchronization can be re-established when the noise subsides, but if the signal set is rotationally symmetric about the origin, the demodulator may resynchronize incorrectly. When a constellation is rotationally symmetric, the value of d(t) is

TABLE I1 CARRIER-PHASE OFFSETAND

4-PSK

Transmitted

Received

sin(mt) sin(wt + 4 2 ) sin(wt + n) sin(wt + 3n/2)

sin(ot + o At) sin(wt n/2 w At) sin(wt n w At) sin(cot 3n/2 o At)

+ + + + + +

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

53

t cos Wt

wt

t

''"'.,.

FIG.23. The effects of phase offset on QPSK.

ambiguous. Certain values of 8(t),the demodulator's estimate of d(t), make the received constellation appear correct even though every re_ceived point is wrong. For the 4-PSK example above, critical values of d(t) - d(t) are 0, n/2,n, and 3n/2 radians. The received constellation appears the same for all four cases, but unless d(t) = 8(t)the decoder fails. We define a constellation to be any finite collection of points in twodimensional Euclidean space. A permutation of a constellation C that preserves distance between points, distance to the origin, and orientation (clockwise/counterclockwise) is a rotation of C . The set of all rotations of C is labeled R,. The set R, forms a cyclic abelian group under function composition. Any 360"/n rotation p E R, is a generator of R,; i.e., { p, p 2 , p', . . .} = R,. A constellation C with an element p E R, of order n is said to be n-way rotationally symmetric. By this definition, a six-way rotationally symmetric constellation is also three-, two-, and one-way rotationally symmetric. We will assume that small changes in d(t) are automatically tracked and corrected. Then, using the above definitions, the effects of phase tracking errors on a trellis code can be represented as a randomly selected rotation 8 E R, appended to the encoder output function M . A change in 8 is called a phase jump; such changes are assumed to be rare. B. Rotationally Invariant Trellis Codes

A direct way to resolve phase ambiguity is to estimate 8 based on the decoder's performance. A simple but error-prone method of finding 8 is to

54

HOWARD J. CHIZECK AND MITCHELL D. TROTT

generate a new estimate randomly whenever the decoder is failing. More complicated procedures are more reliable, but even the best methods require several hundred modulation intervals to reach a confident decision after a phase jump (Zhu and Clark, 1987). Furthermore, sophisticated estimation procedures may unacceptably increase hardware complexity. The best way to handle phase ambiguity is to design the encoder so that choice of 0 is irrelevant. A trellis code transparent to any fixed rotation of the constellation is said to be rotationally inuariant; this occurs if for all valid encoder output sequences { z k } , all rotations of { z k } decode to the same input sequence. In other words, an input sequence that produces {zk} must also be able to produce { o ( z k ) } for every 0 E R,. A more precise condition for rotational invariance is given in the following definition.

Definition 1. A trellis code with an n-way rotationally symmetric constellation C is n-way rotationally invariant if and only if there exist n distinct communicating states r o , . . . ,r, - E S and an element p E R, of order n such that p’(M(f(rO,

UO

‘‘

uk))) = M ( f ( r j ,

U O ’ ‘ ’ uk))

(79)

for all uiE U and k 2 0. The functions M and f are defined in Eqs. (30)-(33). The trellis diagram and constellation of a simple four-way rotationally invariant trellis code is given in Fig. 24. Observe that depending on the initial state, output sequences {O,O,O ,... }, { l , l , l , ...}, {2,2,2,...}, and {3,3,3,... } are all possible, and each corresponds to an all-zero input. An important point of Definition 1 is that rotational invariance is a property of a code’s input-output structure, not its set of reachable output sequences. Definition 1 also implies that all rotationally invariant codes have an infinite input memory, because the current state is not uniquely determined by a finite number of past inputs (see Section V.F). This explains why tools developed to find codes with good free Euclidean distance are ineffective at finding codes that are also rotationally invariant: no finite input memory code is rotationally invariant, and Forney’s canonical class of linear sequential circuits is inapplicable. Moreover, linearity has no natural interpretation in this setting. Restricting attention to “linear” systems merely excludes potentially useful codes. If we survey reported codes, it appears that the best rotationally invariant codes have marginally worse performance than the best non-rotationally invariant codes of the same complexity (Zhu and Clark, 1987). This has been proven (by enumeration) only for state sizes of 8 or less.

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

55

+3

FIG.24. Oerder’s eight-state four-way rotationally invariant trellis code.

C. Diflerentinl Encoding

Most reported rotationally invariant codes are composed of two independent parts: a “differential”precoder, and ordinary trellis code, as in Fig. 25 (the single input arrows in Fig. 25 can represent several parallel binary inputs). A differential encoder for an n-way rotationally invariant trellis code is a modulo n adder with memory. The following equations describe a differential encoder as an FGH: S k + , = Sk

+ b(UJ

(80)

= Sk

+ b(Uk),

(81)

Yk

where sk E Z,, y k E Z,, Uk E U, and b : U long as b(.) is bijective. ...................................................

! Differential encoder

-+ Z,.

..........................................

~

D ................. ....................................

i Differential decoder

Encoder,

- Channel, I

Both U and b(.) are arbitrary, as

.

D

Decodcr <

..................................

.............,

~

-

56

HOWARD J. CHIZECK AND MITCHELL D. TROTT

The trellis code cascaded with the differential precoder must satisfy special conditions for the complete encoder to be rotationally invariant. Methods of constructing differentially encoded rotationally invariant codes are discussed in detail by other authors (Oerder, 1985; Wei, 1984; Zhu and Clark, 1987), so we do not discuss them here. The method of constructing rotationally invariant trellis codes through differential encoding is popular because it reduces decoder complexity. Only the primary trellis code is Viterbi decoded; the effects of the precoder are removed by a simple inverse differential encoder. A four-state precoder cascaded with an eight-state rotationally invariant code has a total of 32 states, but the Viterbi decoder consists of only eight. A more important reason for the popularity of differential encoding is a pragmatic one. With the currently available tools, there is no way to search for any other type of rotationally invariant code. The differential precoder provides the infinite input memory and “nonlinearity” (it’s not an LSC) required for rotational invariance. This allows the trellis code cascaded with the precoder to be an LSC, or to have a finite input memory. Exhaustive enumeration of FIM encoders is possible for small state sizes (Zhu and Clark, 1987). Differential encoding does have some shortcomings. One major disadvantage is error multiplication. By Viterbi decoding only the trellis code, not the precoder, maximum-likelihood estimation is lost. The inverse differential encoder is described by the following equations: Sk*+l

(82)

= uk*

yk* = bK1( -s$

+ u$),

(83)

where y? E U, x? E Z , , uf E Z,, and U, b(.) are defined as in Eq. (80). Examining the state update equation in Eq. (82) shows that the inverse system has a finite input memory with constraint length 1. Hence, any single error in the Viterbi decoder will produce two errors after passing through the inverse precoder. This raises an interesting question: Assuming that error multiplication is acceptable, why consider only differential precoders? Why not use an arbitrary type of precoder that has an FIM inverse with constraint length 1,2, or more? Savings in decoder complexity using differential encoding is not guaranteed. In some cases a trellis code can absorb a differential encoder without increasing in size. For example, Wei’s rotationally invariant eight-state code (see below) has the same d,,,, as Ungerboeck’s non-rotationally invariant eight-state code (see Section 1V.B). This subject has not been thoroughly explored, since few nondifferentially encoded rotationally invariant codes exist.

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

57

As we will see in the next section, FGHs are able to elegantly represent “ordinary” rotational invariance. Unfortunately, finite group homatons do not appear to simplify the analysis of differential encoding, because the cascade of a differential encoder and an FGH is not always an FGH. D . FGH Rotational lnuariance

Definition 1 is readily applied to FGHs, producing the main result of this section. Theorem I3 provides necessary and sufficient conditions for a class of aperiodic FGHs to have rotational invariance without differential encoding. Theorem 13. An FGH weighting pattern with T(u)= e for some u E U and all i 2 0 (i.e., an FGH with a horizontal branch in its trellis diagram, see

Theorem 11) is n-way rotationally invariant if and only if there exist elements r E Y and p E R, of order n such that p ( M ( y ) )= M ( y r)

for all

y

and there exists a sequence of inputs { w,,, . . . ,wj-

T ~ ( W ~ - ~T)k*+ 1 ( ~ j - 2 ) * . . . *

Tk+j-l(wo)

1}

E

Im{f(.)},

(84)

such that for

=r

k 2 t.

(85)

Proof fsuficiency): We must show that the conditions of the theorem guarantee rotational invariance. That is, we must find n communicating states ro,. . . ,r,- that satisfy Eq. (79). Use the FGH weighting pattern to form an SO-realization. Theorem 1 1 tells us that the initial state of the SO-realization so = (e,.. . , e ) is not transient, hence all states reachable from ( e , .. . , e ) communicate. To prove sufficiency we will show that the states r, = (e,. . .,e), r1 = (r,. . . ,r), . . .,r,- = (r”- I , . . . ,r“- ’) satisfy Eq. (79), and we will find an input sequence that proves that r l , . . . ,r, - are reachable from ro. Consider the input sequence composed of i copies of { wo,. . . ,wjfoliowed by t (the periodic delay) copies of u:

,

I

I/

{uo,. . . ,U,+ij-

1}

=

{ho,. . . ,oj-1, .:. ,w 0 , . . . ,wj-;u,. . .,u}.

(86)

This input sequence drives the system from state ro = {e, . . . ,e) to some state x i . From Eq. (53), c(ak(xi))=

K(u)

* ’

‘4

+f

- 1(0)

Tk + t ( w j - 1) .

‘

Ktt

+ i j - 1(wo) (87)

for i, k 2 0. Combining with Eq. (85) and using the assumption that q ( u ) = e for k 2 0 yields c(ak(xi))= ri

(88)

58

HOWARD J. CHIZECK AND MITCHELL D. TROTT

for i, k 2 0. The structure of the a and c homomorphisms of the SO-realization allows Eq. (88) to hold only if x i = ri = (ri,. . . ,ri), thus establishing that r o , . . . , r , - communicate. To show that r o , . . . ,r , _ satisfy Eq. (79),apply induction to Eq. (84) to give P'(M(Y))= M ( y

(89)

Ti)

for i 2 0 and y E Im{ f ( . ) } . Now, combine Eqs. (88) and (51) to see that f(ri?uo"'Uk)=D(Uk)oTO(Uk-l)o"'o

T(UO).ri

=f(ro,uo...uk).ri

(90) (91)

for i, k 2 0 and all ui E U. Since Eq. (89)holds for all y E Im{ f ( . ) } , we can insert Eq. (91) into Eq. (89) to produce Eq. (79). Proof(necessity): We must show that the conditions of the theorem hold for all rotationally invariant FGH weighting patterns with T(u)= e for some u E U and all i 2 0. Definition 1 specifies that there exist n states r o , . . . r,that satisfy Eq. (79). This in turn implies that for any ro E S there exist states r l , . . . r,- that satisfy Eq. (79). Choose ro = (e,. . .,e). From Eq. (51), f ( r o ,u . . . u) = D(u);

(92)

f ( r l ,u...u)

(93)

= ~ ( u0) c(ak(rl)).

Substituting into Eq. (79), we see that p ( M ( D ( v ) ) )= M(D(4 c(a"r1)))

(94)

for k 2 0. The value of the right-hand side of Eq. (94) must be independent of k, hence 4 a k ( r 1 ) )= 0 for k 2 0. Let r

=

(95)

1 )

c(rl). Inserting Eq. (95) into Eq. (51) yields

f(t-1,u o ' " U k ) = D ( U k ) o T O ( U k - l ) o " " = f b . 0 , uo, . . ., U k )

G-l(UO).r

(96) (97)

f

for all uiE U and k 2 0. Now, combining Eqs. (79) and (97) we have that p(M(f(rO,

uO"*uk)))

=

M(f(rO?

UO"'Uk)

r,

(98)

for all ui E U and k 2 0. That is, p ( M ( y ) ) = M ( y r))

for all

y E Im{ f ( e , -I>.

(99)

We must now find and input sequence that satisfies Eq. (85). Definition 1 states that ro and r l communicate, so there exists some input sequence { w o , . . . ,wj-1 } that drives the system from state ro to r l . Combining Eqs. (95)

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE 59

and (53) produces r = T(wj-J.....

T+j-l(wo)

( 100)

for k 2 0. w The requirement that Y have an element of order n insures the existence of n-way symmetry in the output group, while Eq. (84) insures that the output group’s symmetries align with those of the constellation. Usually, Y = Im{f(.)}. Once Eq. (84) is satisfied, the SO-realization of the FGH is guaranteed to have have the states rO,...,r,-, described in Definition 1. Equation (85) merely insures that these states communicate. There are two important consequences of Theorem 13. First, the constraint stated in Eq. (85) forces all rotationally invariant FGHs to have an infinite input memory (see Theorem 9). Second, the requirement that there exist an element of order n proves that LSCs cannot be n-way rotationally invariant unless n is prime. The following two examples were chosen to illustrate the application of Theorem 13, not for their value as encoders. Example; The constellation and function M ( - ) for a four-way rotationally invariant FGH code are shown in Fig. 26. The input set is U = {0,1> and the output group is Y = Z,. The code’s weighting pattern is D(0) = 2,

D(l)=6,

{T(O)}= {0,0,0,0,0,0,0)...} {T(l)}= ( 4 , 5 , 5 , 0 , 2 , 2 , 2,...}

with periodic delay t = 4. Setting D = 0 satisfies the assumption of Theorem 13, while conditions (84) and (85) are satisfied by either r = 2 and wo = 1, orr=6and{wo,w,,w,} ={l,l,l}.

t6 FIG.26. Constellation for example four-way rotationally invariant FGH.

60

HOWARD J. CHIZECK AND MITCHELL D. TROTT TABLE 111 GROUP TABLE FOR D,,THE SYMMETRIES OF A TRIANGLE Po

PI

P2

PI

P2

P3

Po

Po

PI

P2

PI

P2

P3

PI

PI

P2

Po

P2

P3

PI

P2

P2

Po

PI

P3

P1

P2

P1

PI

P3

P2

Po

P2

PI

112

112

PI

P3

P1

Po

P2

P3

/' 3

P2

PI

P2

PI

Po

P*.

FIG.27. Constellation for example three-way rotationally invariant FGH.

Example: The input set and output group for a non-abelian three-way rotationally invariant FGH code are U = (0,1,2) and Y = D 3 ; the group table for D 3 is provided in Table 111. Figure 27 gives the constellation and function M(.). The code's weighting pattern is D(0) = P O ,

('T(0))= ( ~ o , O ~ O ~ O ~ O ~ O , ~ ~ ~ )

D ( l ) = p1,

{'T(l))

D(2) = p29

{T(2))= { ~ 3 , p 0 , p 2 , r u 3 , c 1 3 , r u 3 , . . . )

=

{p11p3,ru1,~1,c11,ru1,...)

with periodic delay t = 3. Conditions (84)and ( 8 5 ) are satisfied with r = p1and wo = l , W , = 2. m Two useful rotationally invariant codes are realized as FGHs in the next examples. Neither code has been previously represented in an algebraic setting.

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATlONAL INVARIANCE 61

Example: In this example we use Theorems 10 and 13 to find an FGH weighting pattern for L. F. Wei’s (1984) “generalized feedback” eight-state 32CR four-way rotationally invariant trellis code. This code is a CCITT international standard for 9600 bps voice-grade communication. Wei’s code is usually described using a state-transition table or a block diagram with nonlinear elements; FGHs are able to represent the code directly. Table IV describes the allowed state transitions and corresponding outputs of the code, where uk, s k , $ + I , and yk are the current input, current state, next state, and current output respectively. Figure 28 depicts the TABLE IV STATE TRANSITION TABLE FOR WEI’SEIGHT-STATE ROTATIONALLY INVARIANTCODE Uk =

sk

’k+ I

0

Uk = vk

Sktl

1

Uk

yk

sk+l

=

2

Uk

Yk

‘I+ 1

=

3 Yk

62

HOWARD J. CHIZECK AND MITCHELL D. TROTT

constellation and function M(.). Each output element { A ,B , . . .,H ) specifies a set of four points in the constellation; two additional uncoded bits select one point of the four. First, we assume that the code is an FGH. Its weighting pattern can then be determined from Eqs. (74) and (75) of Theorem 10: D ( 4 = f(0,U) T(U)

=

(101)

f(o,pq)-'

f(0,yO ;. .O)

i+ 1

(102)

if1

for i 2 0. We can also assume, without loss of generality, that A is the identity element (see Theorem 2). Since f(0,O.. .0) = A, Eqs. (101) and (102) simplify to D ( 4 = f(0,U)

(103)

T ( u ) = f(0,pO;* ' Q).

( 104)

i+ 1

The weighting pattern is found by determining the values off from Table IV: D(0) = A,

{T(O))= { A , A , A , A,...}

D(2) = B,

{ T(2)} = { C, C, C, C, . . .)

D(3) = D,

{T(3)} = { E , G , G , G,...}

We must now find the group Y = ( { A , .. . ,H}, 0 ) . The smallest two possibilities are Y = Z, x Z, and Y = Z,. Either will do, but Y = Z, x Z, seems more natural for four-way rotational invariance. We have already assumed that A = (0,O). Since rotating A by 90" (clockwise) results in G , Eq. (84) requires that G have order 4. Let r = G = (1,O). The sets C and E are 180" and 270" rotations of A , hence C = rz = (2,O) and E = r 3 = (3,O). Any remaining element can be assigned to B; we'll use B = (0,l). This fixes H = (1, I), D = (2, I ) and F = (3,l). Equation (85), the last requirement of Theorem 13, is trivially satisfied with w o = 3. The two uncoded input bits select one point from each set of four points { A , .. . ,H } . This is indicated in Fig. 28 by a subscript attached to each label. The subscripts are chosen so that Gi, Ci, and Ei are 90°, 180", and 270" rotations of A i . The subscripts for B, D, F, and H are chosen similarly. The SO-realization can now be formed according to Eqs. (54)-(57) with periodic delay t = 1 and period r = 1. The input set is U = (0, 1,2,3}, the state group is S = ((Z, x Z,) x (Z, x Z2),+), and the output group is Y = (Z, x z,, +): a:S

-+s

9

( Y o o ~ Y l o ~ Y o l ~ YH l l )( Y 0 1 ~ Y 1 1 , Y O I ~ Y 1 1 )

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

b:U

+S,

0 H (0,0, 0,O)

63

2 H (2,0,2,0)

1 ~(1,0,3,0) 3~(3,0,l,O) r:S

+

(Yoo~Ylo~Yol~YlJ(YlO~YOO)

y,

d:U+Y,

Ow(0,O)

2~(0,1)

1

3 H (2,l).

H

(2,O)

The SO-realization for this code is inefficient, having 56 unreachable states. A smaller (minimal) realization, with S = (Z, x Z,, +), can be generated by inspection:

We can now verify that this FGH actually corresponds to the code in rn Table IV. Example: Oerder’s (1985) eight-state four-way rotationally invariant trellis code for a 4-PSK constellation is shown in Fig. 24. An FGH realization with input set U = {O,l),state group S = Z, x Z,, and output group Y = Z, can be generated by inspection:

a:S -+S,

(x,,x,)

b:U+S,

OH(O,O)

+

(x0,O)

c:S

-+

Y,

d:U+Y,

(xo,x,)

0-0

-

xo

+ X I + x1

1H2

1 H( 1 9 1 )

The corresponding weighting pattern is D(0) = 0,

{ T ( 0 ) )= {O,O,O,O,. . .}

D(1) = 2,

{T(l)}= { 3 , 1 , 1 , 1 , ...},

which clearly satisfies the conditions of Theorem 13. Since the conditions of Theorem 13 are expressed as constraints on weighting patterns, it is possible to enumerate rotationally invariant FGH trellis codes. In Section VII we describe how to do this.

64

HOWARD .I.CHIZECK AND MITCHELL D. TROTT

VII. FINDING NEWCODES In this section we show how to apply the results of the previous sections to find new codes. We then describe several new (nondifferentially encoded) rotationally invariant codes for 8- and 12-PSK constellations. The method we use to search for new codes is simply an enumeration over a specified class of weighting patterns. Each weighting pattern in the search class is used to generate an FGH trellis code, which is then tested for free Euclidean distance and catastrophic error propagation. The best codes encountered during the search are retained. FGH trellis codes are harder to enumerate than LSC trellis codes because the class of FGHs is so much larger. We keep the search class to a manageable size by avoiding weighting patterns with transient or noninvertible behavior. We also simplify enumeration by including only those weighting patterns that are guaranteed to have a specified degree of rotational invariance. For example, using FGHs it’s easy to search through a set of 16 million trellis codes, each of them eight-way rotationally invariant. Ideally, one would like to search for FGH trellis codes with a specified number of states. Since we have no a priori method that determines the size of a trellis code from its weighting pattern, there is no obvious way to be certain when all FGHs of a particular size have been found. We must simply try more and more complicated weighting patterns and hope for the best. Because rotationally invariant trellis codes are a subset of “ordinary” trellis codes, one might expect that the best rotationally invariant codes will have lower free Euclidean distance than codes that are not so constrained. With some exceptions, our limited code searches have suggested that this is indeed the case. The method we used to enumerate FGH trellis codes is divided into several steps, itemized below. An incremental example is given at each step to help clarify the design process. 1. Select the input set. The important characteristic of the input set is its cardinality; the elements of the input set have significance only for mnemonic purposes. In our example we will use a two-bit binary input represented by the set {00,01,10,11>,though any other four-element set would d o as well. 2. Select the constellation. The choice of constellation is crucial to code performance, but we will not attempt to address this complicated issue here. Interested readers are referred to Forney et al. (1984) and Forney (1988).We choose an 8-PSK constellation for our example. 3. Choose the amount of rotational invariance desired. One generally wants the highest degree of rotational invariance possible for a given constellation. However, a high degree of rotational invariance usually (but not

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

65

always) degrades code performance. The exact penaties for n-way rotational invariance are hard to predict. We have observed that two-way rotational invariance can often be achieved at no cost, while four-way invariance degrades performance to the level of a non-rotationally invariant trellis code with half as many states. An exception is Wei's (1984) eight-state four-way rotationally invariant code, which has the same performance as its eight-state non-rotationally invariant cousin. Trellis codes with eight-way rotational invariance typically perform at a level comparable to that of a code one-fourth their size. An exception is given below. Large codes (64 or more states) may allow a high degree of rotational invariance without penalty. This remains an open question. For our example we are interested in eight-way rotational invariance, the maximum possible for an 8-PSK constellation. 4. Select the output group. Commutative groups that have the same number of elements as the constellation seem to produce the best codes. The utility of output groups larger than the constellation is doubtful, but nonabelian groups may merit further investigation. We have also found that the order of the elements in the group should be as low as possible. Since eightway rotational invariance requires an element of order 8, for our example we will use the group Z,. Appropriate choices for four- and two-way rotational invariance would be Z, x Z, and Z, x Z, x Z,, respectively. 5. Label the points (or cosets) in the constellation with the elements of the output group. This determines the function M. To satisfy Theorem 13, M must be chosen so that p ( M ( y ) )= M(y + r) for all y E Y, where p E R, and r E Y are elements of order 8. Let r = 1 and p = 45" (clockwise). Any point can be labeled with the element 0, but the relative labeling of the remaining points is fixed to that shown in Fig. 29. 6. Choose the period and periodic delay for the set weighting patterns to enumerate. This choice determines the number of states in the SO-realization, which upper bounds the number of reachable states in the code. For our

. 4

0

FIG.29. 8-PSK constellation labeled with Z,.

66

HOWARD J. CHIZECK AND MITCHELL D. TROTT

example the period and periodic delay with both be 1. Our best codes all have period 1, and we have observed that periodic delays greater than 2 produce excessively large codes (more than 64 states). 7. It’s important to simplify enumeration by filling in as many empty “slots” in the weighting pattern as possible. The D function, for example, can usually be selected in advance. Ungerboeck’s set-partitioning heuristics (see Section 1V.C) suggest that for an 8-PSK constellation, Im{D(-)} = {0,2,4,6}. This choice of D causes the labels on the branches leaving each trellis node to be selected from either {0,2,4,6} or { 1,3,5,7}. It also insures 0-delay invertibility (see Corollary 7). Several more slots are filled in by constraining the weighting pattern to insure rotational invariance. Theorem 13 requires that for some u E U, q ( u ) = 0 for i 2 0. Set T(0)= 0. Theorem 13 also demands that there exist an input sequence {wo,. . . ,wj- such that

C ( W ~ - ~ ) . . .C. *+ j - , ( w o ) = r

(105)

for k 2 t . In our example, r = 1, t = 1 and r = 1, hence constraint (105)will be met if and only if q ( u ) is odd for some u E U. We choose (arbitrarily) to set T,(2) = 1. Here is the weighting pattern thus for:

The five unknown slots are indicated by xo,. . .,x4. Each slot can assume eight different values, for a total of 8 5 = 32,768 different eight-way rotationally invariant trellis codes. The final step is to search through this collection of codes to find the best ones. Enumeration proceeds roughly along these lines: 1. Select the next weighting pattern from the set and generate its SOrealization. 2. Walk through the SO-realization to find all reachable states. All states are guaranteed to be distinguishable, and as long as transients states are avoided all reachable states will communicate. (Rotationally invariant FGHs generated from Theorem 13 never have transient states.) 3. Generate a state-transition table using the list of reachable states and the SO-realization.

67

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

4. Find the free Euclidean distance of the code, check for catastrophic behavior, then save the code if it’s better than any previously found code with the same number of states. 5. Repeat.

Applying this method of enumeration to our example resulted in several interesting codes, including a 16-state eight-way rotationally invariant code with the same performance as Ungerboeck’s eight-state code (3.6 dB). The weighting pattern of the 16-state code is

D(0) = 0,

T(0)= (O,O, O,O,. ..)

D(1) = 2,

T(1) = { 5 , 3 , 3 , 3 , . .,)

D(2) = 4,

T(2) = 13, 1,1,1, ...}

D(3) = 6,

q ( 3 ) = {2,2,2,2,.. .}

The state transition table for this code, generated directly from the SOrealization, is given in Table V. Intriguingly, this code has no minimal FGH realization. The results of several additional code searches for 8-PSK and 12-PSK constellations are summarized in Table VI and Table VII. The degree of TABLE V STATE TRANSITION TABLE FOR A N S-PSK, 16-STATE. EIGHT-WAYROTATIONALLY INVARIANT CODE Uk

sk

sk + I

=

0

Uk

Yk

0 2 I

3

sk

+1

=

I

Uk

1’1

2 4

3 5

2 4 3 5 4 6 5 7 6

4 6

0

2

5 7 6 0 7

St+ I

=

2

Uk

Yk

4 6 5

7 6 0 7 I 0 2 1

7

1

3 2 4 3

1

3

5

I 0

sk+ I

=

3 Yk

6 0 7

I 0 2 1 3 2 4 3 5 4 6 5 7

68

HOWARD J. CHIZECK AND MITCHELL D. TROTT TABLE VI ROTATIONALLY INVARIANTCODESFOR 8-PSK, 2 BITS/SYMBOL RI

States

Coding gain, dB

1 1 1 1 1 2 2 2 2 4 4 4 8 8 8

4* 8* 16* 32’ 64* 4* 8* 16* 64 8* 16 32 8 16 64

3.01 3.60 4.13 4.59 5.01 2.00 3.01 4.13 5.01 2.00 3.60 4.13 1.12 3.60 4.13

Output group

z, x z, x z, 2, x 2, x z, z, x z, x z, z, x z2 x z, z, x z, x 2, z, x 2, x z, 2, x z, x z, z, x z, x z, z, x z, x 2, z4 x 2 2 z4 x z2 24

x

z2

z0

Z8

z0

TABLE VII ROTATIONALLY INVARIANT CODES FOR I2-PSK, 2 BITS/SYMBOL

R1

States

Coding gain, dB

output group

4 4 4 12 12 12

12 24 48 12 24 48

2.13 3.29 3.81 1.76 3.29 3.81

z, x z4 2, x 24 z3

z 12 z12

x

z4

Z I2

rotational invariance of each code is indicated in the “RI” column; previously known codes are indicated with an asterisk (*). The searches were by no means exhaustive, hence there is no guarantee that any of these codes are optimal. Moreover, the codes were chosen based solely on free Euclidean distance, not on bit error rate or other more realistic measures. The 12-PSK codes are largely uninteresting. They are included here mainly to demonstrate the ability of FGHs to represent unusual codes.

ALGEBRAIC SYSTEMS, TRELLIS CODES, AND ROTATIONAL INVARIANCE

69

The computational effort required to find FGH codes escalates rapidly with the cardinality of the input set, the cardinality of the output set, and the number of states in the codes searched. Our longest runs (20 million FGHs) consumed up to 48 cpu hours on a VAX 8800, using reasonably optimized algorithms written in C. Since many of the FGHs considered in a typical search are in some sense “equivalent,” a code search could be greatly speeded by developing ways to eliminate these equivalent codes. Some limited conclusions can be drawn from our results. In general, the greater the required rotational symmetry, the lower the resulting free Euclidean distance. Exceptions include the 16- and 64-state two-way rotationally invariant codes and the 16-state eight-way rotationally invariant code. We have found that codes with an unusual number of states are uniformly useless. For instance, none of the 24-state eight-way rotationally invariant codes found in our searches were superior to those with 16 states, so we did not include them in the tables. Since heuristics play a large part in FGH code design, particularly in the selection of the output group and the class of weighting patterns to enumerate, many types of FGH codes remain unexplored.

VIII. OPENQUESTIONS We conclude with some of the many remaining open questions.

Is it possible to determine trellis code performance directly from an FGH weighting pattern? This is not an easy problem even for LSCs and generator polynomials. The complex iterations between the geometry of the constellation and the transitions in the encoder make a simple solution unlikely. Is there a way to factor a “precoder” out of rotationally invariant FGH trellis codes? This would provide a means of finding differentially encoded rotationally invariant codes (assuming that differential encoding can actually enduce code complexity, which is not certain). Cascading of FGHs (or, more likely, FGHs and FGHSSs) is probably most promising way to proceed. How can we decide how many reachable states an FGH will have by examining its weighting pattern? This may not admit a simple solution: Consider that a linear congruential random number generator is an FGH. We need more ways to reject FGHs in a code search. It is certain that many FGHs considered using the enumerative methods of Section VII are in some sense equivalent. Only one should be tested. For arbitrary trellis codes this may be difficult, but rotationally invariant trellis codes have a great deal of structure.

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HOWARD J. CHIZECK AND MITCHELL D. TROTT

An algebraic way to check if an FGH weighting pattern is catastrophic would be helpful. Again, this may be possible for rotationally invariant codes even if it isn’t possible for FGHs in general. More general conditions for rotational invariance that don’t require a horizontal branch in the trellis code would be useful. However, all (known) good codes have horizontal branches, and several FGH code searches did not reveal any counterexamples. Are codes with a nonzero inverse delay useful? Is there a general way to align the group structure of a constellation with the output group of an FGH, even when rotational invariance is not important?

REFERENCES Aulin, T. and Sundberg, C. W. (1981a). “Continuous phase modulation-Part I: Full response signaling,” I E E E Trans. Commun.COM-29, 196-209. Aulin, T. and Sundberg, C. W. (1981b).“Continuous phase modulation-Part 11: Partial response signaling,” I E E E Trans. Commun. COM-29,210-225. Berlekamp, E. R. (1968). Algebraic Coding Theory, McGraw-Hill Book Company, New York, New York. Berlekamp, E. R., Peilie, R. E., and Pope, S. P. (1987). “The application of error control to communications,” I E E E Commun. Magazine 25 (No. 4), 44-57. Biglieri, E. (1984). “High-level modulation and coding for nonlinear satellite channels,’’ I EEE Trans. Commun.COM-32,616-626. Biglieri, E. (1986). “Ungerboeck codes do not shape the signal power spectrum,” I E E E Trans. Inform. Theory IT-32,595-596. Brockett, R. W. and Willsky, A. S. (1972).“Finite group homomorphic sequential systems,” I E E E Trans. on Automatic Control AC-17,483-490. Calderbank, A. R. and Mazo, J. E. (1984).“A new description of trellis codes,” I E E E Trans. Inform. Theory IT-30,784-791. Calderbank, A. R., Mazo, J. E., and Wei, V. K. (1985).“Asymptotic upper bounds on the minimum distance of trellis codes,” I E E E Trans. Commun.COM-33, 305-309. Calderbank, A. R. and Sloane, N. J. A. (1987). “New trellis codes based on lattices and cosets,” I E E E Trans. Inform. Theory IT-33,177-195. Chizeck, H. J. (1976). “Inverses and coding applications for systems evolving in finite groups,” M.S. Thesis, Dept. of Systems Eng., Case Western Reserve University, Cleveland, Ohio. Chizeck, H. J. (1978).“Inverses of finite group systems,” I E E E Trans. on Automatic Control AC-23, 66- 70. Divsalar, D., Simon, M. K., and Yuen, J. H. (1987).“Trellis coding with asymmetricmodulations,” IEEE Trans. Commun. COM-35, 130-141. Forney, Jr., G . D. (1970). “Convolutional codes I: Algebraic structure,” l E E E Trans. Inform. Theory IT-16,720-738. Forney, Jr., G . D. (1973).“The Viterbi algorithm,” Proceedings of the l E E E 61,268-278. Forney, Jr., G. D. (1988). “Coset codes-Part I: Introduction and geometrical classification,” I E E E Trans. Inform. Theory IT-34,1123-1151.

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Forney, G . D., Jr., Gallager, R. G., Lang, G. R., Longstaff, F. M., and Qureshi, S. U. (1984). “Efficient modulation for band-limited channels,” I E E E J . Selected Areas Commun. SAC-2, 632 - 647. Fraleigh, J . B. (1982).A First Course in Abstract Algebra, 3rd Edition. Addison-Wesley Publishing Company, Reading, Massachusetts. Gardiner. C. F. (1986). Akgebraic Structures. Halsted Press, New York. Jacobs, 1. M. and Berlekamp, E. R. (1967).“A lower bound to the distribution of computation for sequenrial decoding,” I E E E Trans. Inform. Theory IT-13, 167- 174. Karpen, M. E. (1986). “Algebraic systems and the structure of DNA,” M.S. Thesis, Dept. Biomedical Eng., Case Western Reserve University, Cleveland, Ohio. Karpen, M. E. and Chizeck, H. J. (1987).“Algebraic systems theory and DNA,”Tech. Rep. R-CZ87-5. Depts. Biomedical and Syst. Eng., Case Western Reserve University, Cleveland, Ohio. Massey, J. L. and Sain, M. K. (1967). “Codes, automata, and continuous systems: Explicit interconnections,” I E E E Trans. o n Automatic Control AC-12,644-650. Massey, J. L. and Sain, M. K. (1968). “Inverses of linear sequential circuits,” I E E E Trans. on Computers C-17, 330-337. Mulligan, M. G. and Wilson, S. G. (1984). “An improved algorithm for evaluating trellis phase codes,” I E E E Trans. Inform. Theory IT-30, R46-851. Oerder, M. (1985). “Rotationally invariant trellis codes for mPSK modulation,” I E E E Int. Coqf. Commun..Con]: Rec.. 1985, pp. 552-556. Ruiz, A. and Cioffi, J. M. (1987).“A frequency domain approach to combined spectral shaping and coding,” I E E E Int. Conf. Commun., Con]’. Rec.. 1987, pp. 1711-1715. Shannon, C. E. (1948).“A mathematical theory of communication,” Bell Syst. Tech. J . 27 379-423, 623-656. Thompson, T. M. (1983). From Error-Correcting Codes through Sphere Packings t o Simple Groups. The Mathematical Association of America. Trott, M. D. (1988).“Finite state algebraic systems and trellis codes,” M. S. Thesis, Dept. Systems Eng., Case Western Reserve University, Cleveland, Ohio. Ungerboeck, G . (1982). “Channel coding with multilevel/phase signals,” I E E E Trans. Inform. Theory IT-28, 55-67. Ungerboeck, G . (1987).“Trellis-coded modulation with redundant signal sets, part 11: Slate of the art,” l E E E Cummun. Magazine 25 (No. 2), 12-21. Wei, L. F. (1984). “Rotationally invariant convolutional channel coding with expanded signal space-Part 11: Nonlinear codes,” I E E E J . on Selected Areas in Commun. SAC-2, 672-686. Willsky, A. S. (1973). “Dynamical systems defined on groups: Structural properties and estimation,” Ph.D. Thesis, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts. Willsky, A. S. (1975).“Invertibility of finite group homomorphic sequential systems,” Inform. and Control 27, 126-147. Wilson, S. G., Sleeper, H. A,, 11, Schottler, P. J., and Lyons, M. T. (1984). “Rate 3/4 convolutional coding of 16-PSK: Code design and performance study,” I E E E Trans. Commun. COM-32. 1308- I3 14. Wozencraft, J. M. and Jacobs, 1. M. (1965).Principles cf Communications Engineering. Wiley. New York. Zehavi, E. and Wolf, J . K. (1987). “On the performance evaluation of trellis codes,” I E E E Trans. Inform. Theory IT-33, 196-202. Zhu, Z. C. and Clark, A. P. (1987). “Rotationally invariant coded PSK signals.” I E E Proc. Pt. F 134.43- 52.

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ADVANCES IN ELECTRONICS A N D ELECTRON PHYSICS.VOL 79

Topography of Solid Surfaces Modified by Fast Ion Bombardment D. GHOSE AND S. B. KARMOHAPATRO Sahu Institute of Nucleur Physics Culcurtu, India

I. Introduction . . . . . . . . 11. Basic Ion Bombardment Processes . A. Ion Penetration and Stopping . B. Channeling. . . . . . . . C. Sputtering . . . . . . . . D. Radiation Damage . . . . . 111. Ion-Induced Surface Modifications . A.Cone.. . . . . . . . . B. Faceting. . . . . . . . . C. Blistering . . . . . . . . IV. Summary. . . . . . . . . . Acknowledgments. . . . . . . References . . . . . . . . .

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107 124 144 146 146

I . INTRODUCTION Fast ion bombardment modifies the topography of solid surfaces as a result of a number of different effects, the most important being the sputtering. Since the surfaces are not always perfectly planar, the variation in sputtering yield with angle of ion incidence causes the surface to be eroded more rapidly where the angle of incidence is higher. Also, the presence of impurities on the surface, the inhomogeneity of the target material, and radiation damage lead to nonuniform etching of the surface. All these result in the development of surface structures. The second effect that can give rise to changes in surface topography is caused by implanation of insoluble gas ions. The phenomenon called radiation blistering is most easily observed with light ions, principally hydrogen and helium, because their range is large compared with the depth of erosion during bombardment and it is therefore possible to accumulate high gas concentrations in the near-surface region before the gas is released by erosion. The formation of voids caused by radiation damage also contributes to the modification of surfaces in some cases. The interest in the studies of the modifications of surface topography by ion bombardment stems partly from the intrinsic fundamental aspects of ion-solid interaction processes and partly from the possible technological applications. 73

Copyright 01990 by Acddernlc Press. Inc All nghts of reproductlon in any form reserved ISBN 0-12-014679-7

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Since the initial observation of sputtering process in glow discharge tubes by Grove in 1852,it has become increasingly recognized that the phenomenon causes both atomic-scale and larger-scale morphological changes on surfaces. As the dose of the bombarding ion increases, the surface of the solid is eroded away successively and then some characteristic etch patterns, such as conical protrusions, grooves, and pits are developed on the surface of the sputtered area. In early investigations, the existence of surface structure was detected by studying the light reflected from the surface. The presence of structures with certain dimensions was indicated by the occurrence of Rayleigh scattering. These observations were subsequently supplemented by optical microscopy, though many of the features were beyond the resolution of these microscopes. Later, the electron microscope was used, involving both the replica and scanning techniques. The resolution limit was in that way extended below 1000 A. The practical resolution limit of the scanning electron microscope (SEM) is, however, -100 A. With the advent of the scanning tunneling microscope (STM), it is now possible to study subnanometer- or atomic-scale topography (Feenstra and Oehrlein, 1985a,b; Wilson et al., 1989). It may be mentioned that the scanning ion microscope (SIM), besides its application to elemental localization by secondary ion mass spectrometry, can also be used to obtain high-quality images of the surface topography by collecting ioninduced secondary electron or ion signals (Levi-Setti et al., 1983, 1986). Using finely focused beams from liquid metal ion sources (Ga), one can obtain lateral resolution of -200 A. Fetz (1942) was the first to discover the dependence of sputter yield on angle of ion incidence. For thin wires sputtered in a low-pressure plasma, sputtering yields were always found to be above the corresponding values for plane targets. One of the implications of this observation, the formation of submicroscopic surface cones, was reported in the same year by Giintherschulze and Tollmien (1942). Textured surfaces formed by ion beam sputtering have a number of characteristic properties that make them suitable for a large and diversified number of applications. Auciello (1981, 1984a, 1986) listed the following fields in which texturing has possible applications and relevances: (i) microelectronics, (ii) surface acoustical and optical technologies, (iii) solar energy conversion technology, (iv) ion beam surface analysis, (v) thermonuclear fusion, (vi) field ion emission and electron microscopy, (vii) surface-enhanced Raman scattering spectroscopy, and (viii) biomedicine (implantology). It has been demonstrated that textured surfaces already are used in some technologies, have the potential to be useful in others, and are relevant on either a detrimental or a beneficial basis in various experimental techniques. The emphasis on blistering studies, in the 1970s, arose mainly from its potential importance in the erosion of the inner walls of the controlled

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thermonuclear reactors (CTR) exposed to ion bombardment (D, T, and He) from hot hydrogenic plasmas. The erosion of the wall surface due to blistering and flaking is orders of magnitude higher than that due to sputtering and introduces heavy impurity atoms, which has the detrimental effect of cooling down the plasma by radiative collision processes. In a CTR machine, the first wall will be bombarded by thermalized helium ions escaping the plasma edge (the temperature of which is nearly 100 eV) and by the nascent 3.5 MeV helium ions from the D-T reaction, which have some probability of directly escaping the magnetic field. The thermalized ions, having a broad angular distribution, are very unlikely to blister the surface (Behrisch and Scherzer, 1983). They mainly contribute to wall sputtering. In contrast, the high-energy helium ions have a high probability of causing surface modifications by blistering, exfoliation, and flaking. Blister formation from the hydrogen isotopes is, however, unlikely for the ion dose rates and wall temperatures found in practice. Recently, a new branch of materials science called plasma surface interaction (PSI) has emerged, which includes various atomic collision processes of plasma particles (ions and charge exchange neutrals) with the first wall structures. The surface deformations induced by high-fluence helium implantation is a narrow field of PSI, and a number of experiments are aimed at assessing the helium-induced blistering problem by bombarding monoenergetic beams of helium ions on a large variety of probable (and improbable) first wall materials. Aside from the technological implications, these experiments have permitted a better understanding of basic phenomena in ion-solid interaction processes (Ullmaier, 1983). A n important parameter for the understanding of bubble growth processes and the subsequent formation of blisters on helium-irradiated materials is the pressure or density of helium in the bubbles. The most direct method for characterizing He bubbles in metals is transmission electron microscopy (TEM). The other methods, which give indirect information, are small-angle x-ray (SAXS) or neutron (SANS) scattering, and the spectroscopic techniques such as vacuum ultraviolet absorption spectroscopy (VUVAS) and electron energy-loss spectroscopy (EELS). A discussion of various experimental methods can be found in the article by Donnelly (1985). The surface modifications due to gas pressure in the bubble can be investigated by optical microscopy and also by SEM. They are often combined with nuclear methods such as Rutherford backscattering spectroscopy (RBS) and nuclear reaction analysis (NRA) to yield information about blister lid thickness and depth profiles of implanted helium. (See, for instance, Scherzer e l al., 1983.) In the present work, following fundamental aspects of ion-solid interactions, the ion bombarded surface modifications in the form of cones, faceting, and blistering are reviewed, along with the progress of the subject in recent years.

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11. BASICION BOMBARDMENT PROCESSES

A . Ion Penetration and Stopping

When a beam of fast ions encounters a solid target, a fraction of the ions backscatters from the surface, while most of the ions penetrate and lose energy in the solid until their energy has fallen below about 24 eV, when they become trapped by the cohesive forces of the solid. The slowing down of the penetrating ion is due mainly to inelastic electronic and elastic nuclear collision processes. The first type of interaction occurs at high energies where the velocity of the projectile is generally greater than the orbital velocity of the lattice electrons, resulting in excitation and ionization processes of both the incident projectile and the target atom, and the collision is said to be inelastic in the sense that the total kinetic energy of the participating particles is not conserved. On the other hand, the second type of interaction, i.e., the elastic nuclear collision, is more frequent at low energies and involves the mechanics of hard-sphere collision between incident ion and lattice atom. In general, the stopping of an energetic projectile in a solid is caused by the sum of these two components; the importance of one over the other is, however, dependent on energy. The varieties of physical phenomena observed during ion bombardment of solids all originate from the energy expended by the ions in the solid. The path length of penetration R , , i.e., the range of the projectile into a solid, is related to the total stopping power by the relation dE’ (-dE’/dx),’

where ( - dE’/dx), is the total stopping power or the specific energy loss

(-,):

(-

(-

+ ~)..c...i.‘ Since energy is lost by the projectile in a series of discrete collisions, the specific energy loss and consequently the path length have a statistical spread of values leading to a near-Gaussian type of range distribution. The trajectory of the penetrating ion is almost straight when electronic stopping dominates, but it follows a zigzag path as it is slowed down by nuclear collisions. As a result, at lower energies, the projected range R , measured along the incident ion direction can be considerably less than the total path length or range, R , . The projected range and the straggling both parallel ( A R , ) and perpendicular ( A R , ) to the ion direction are more useful practical range parameters than those relating to the total path length. =

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For light ions such as H, D and He at energies that are not too low, ( - dE’/dx)e,ec,ronic >> ( -dE’/dx)nuc,ear. A useful rule of thumb is that the en-

ergy loss is predominantly electronic whenever the energy of the bombarding particle in keV is greater than its atomic weight. For energies that are not too high, the electronic stopping cross-section is proportional to projectile velocity, the specific dependence (Lindhard and Scharff, 1961) being given by

Here, Z , and Z 2 are the atomic numbers of projectile and target, respectively. The projectile velocity is v, e is the electronic charge, and a, and uo the Bohr radius of the hydrogen atom and the Bohr velocity respectively. The data for hydrogen and helium stopping powers and ranges in all elements have been compiled by Andersen and Ziegler (1977; Ziegler, 1977).

B. Channeling A number of processes occur during ion bombardment of solid targets, e.g., sputtering of solid and its damage, backscattering, energy loss of ions, secondary electron emission, x-ray production by inner-shell ionization and nuclear reactions. If the solid is homogeneous and isotropic, the results of the interaction of ions with the solid will not be influenced by the direction of the beam and the target. When the target is a single crystal, the interaction will be strongly dependent upon the relative orientation of the crystal and the ion beam. The effect is due to the channeling of ions through crystals, and it is dependent upon the degree of inhomogeneity, anisotropy, and lack of randomness of the crystalline solid. Lindhard (1965) developed a continuum model of directional effects in which the potential of a row or plane of atoms is considered as smeared out, forming a continuous potential. When a charged particle moves along a major crystallographic direction, under certain conditions it may not be able to feel the interaction caused by individual atoms sitting at various lattice sites, but rather experiences a collective effect of all the atoms sitting along a particular axial or planar direction, so that the moving particle will experience the action of potentials associated with continuous strings or planes. A channeled particle loses energy only by electronic collisions, and since it cannot come close to atomic positions, all physical effects that require a close collision between the projectile and target atom are greatly reduced. Axial channeling can be established only for ions incident at less than a critical angle II/ with respect to a row of lattice atoms. For low projectile

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D. GHOSE AND S. B. KARMOHAPATRO

energies this angle is given by (Lindhard, 1965)

where d’ is the distance between the atoms along the axis, E is the incident energy, and uTF is the Thomas- Fermi screening radius. Typical critical angles of keV heavy ions are of the order of ten degrees. The continuum scattering from planes is somewhat weaker and less well defined than for strings of atoms, because in the plane, the distance between scattering centers is random. Lindhard (1965) proposes that the continuum scattering remains valid so long as the maximum angle of deflection in any single collision at a distance y from the plane does not exceed the transverse angle required to reach y. This leads to slowly varying values of the distance of minimum approach, generally of the order of the screening length uTF at high energies, and increasing with decreasing energy. Because of the relatively slow variation of the continuum potential, Y(y), with y, it is assumed that the potential barrier of a plane is not higher than Yefr = Y(0)/2.However, for quite low energies, the barrier becomes somewhat lower than the above value. The concept of channeling is applied to predict the cone apex angle, which is described in Section III.A.4. C . Sputtering

Sputtering, i.e., the ejection of atomic and molecular particles, is known to be a universal phenomenon, which occurs when a solid target is bombarded with energetic ions. The most essential quantity to characterize the sputtering effect at a solid surface is the sputtering yield or the sputtering ratio S , i.e., the average number of atoms ejected per incoming ion. S depends on a number of parameters, e.g., ion energy, type of the incident ion, angle of incidence, material to be sputtered, target temperature, surface condition and, if single crystals are used, the orientation of the exposed crystal face. The experimental values of S lie usually in the range between 1 O - j and 10” atoms/ions, dependent on ion and target (Andersen and Bay, 1981). The phenomenon of sputtering in an isotropic solid can be understood qualitatively in the following way: When a projectile enters a solid target, it collides several times with the target atoms and creates a generation of primary recoil atoms, also called primary knock-on atoms (PKA). The recoils that have sufficient energy are able to transfer momenta to other target atoms, thereby creating another generation of recoil atoms, and so on. During slowing down, the projectile may also backscatter towards the surface and again produce recoils along its path. In this way, a collision cascade is

-

-

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79

generated in a space-time frame of reference. The recoil target atoms that lie close to the surface and have sufficient energy to overcome the surface binding energy will leave the surface. Sigmund (1969a) developed a theory of sputtering for random targets within the framework of transport theory. He showed that the sputtering yield at depth x is given by s(x) = A * F D ( ~ ) ,

(5)

where A is a material constant and F,(X) is the deposited energy distribution function. A is given by

where N is the density of target atoms and V, the surface binding energy. For the case of backsputtering, x = 0 and FD(0)is mathematically expressed by the formula FD(o)

= aD(M2/Ml

9

?) ’

’ Sn(E),

(7)

where S n ( E ) is the nuclear stopping cross-section and aD is a dimensionless quantity depending on the mass ratio between the target atom mass M, and the impinging ion mass MI and the angle of incidence 6, (q = cose). For perpendicular incidence of the bombarding particles, i.e., for cose = 1, S is given by S

= 0.042-

aDSn(E)

v,A2

.

The ciD function in Sigmund’s theory determines the multiple-scattering character of the sputtering phenomenon, and it plays a decisive part when the variation of yield with angle of incidence is studied. In a single-scattering theory, the yield is expected to rise as

simply because of the longer pathlength close to the surface, while the dependence within the multiple-scattering-based theory is expressed through the ciD function. For not-too-oblique ion incidence, Sigmund gives

where m

‘Y

3 for M2/Ml 5 3, and m tends to unity for M , << M , .

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D. GHOSE AND S. 8. KARMOHAPATRO

The angular dependence of S plays the prime role in the development of conical protrusions on sputtered surfaces, which is discussed in Section III.A.2. In the case of monocrystalline sputtering, there is a considerable influence of the lattice structure on the collision cascade. In the later stages of the development of collision cascade, when the energy of the knock-on lattice atoms has fallen to below about 100 eV, the kinds of collisions that occur are extremely sensitive to the lattice structure, as the mean free path is roughly equal to the lattice spacing. Silsbee (1957) suggested that under these conditions, correlated sequences of collisions would propagate along closepacked lines of atoms in the crystal, and the atoms would be ejected preferentially along those directions. The experimental observations of the preferential ejection of sputtered atoms from monocrystals indeed suggest that the sputtering process in monocrystals is mainly governed by these correlated processes. D. Radiation Damage

The radiation-damage phenomena are classified as displacement damage or impurity damage according to the type of interactions between the radiation and lattice atoms: (i) The bombarding particles transfer recoil energy E , to the lattice atoms. If E , exceeds the value Ed, the threshold energy for displacement, a vacancy-interstitial pair is created provided that the displaced atom moves far enough from the vacant site to avoid recombination. In the second step, the energetic primary knock-on atoms (PKA) produce a cascade of point defects that is called a displacement cascade. When the kinetic energy of the colliding atoms has dropped below E d , the displacement events stop. However, the energy per atom in the cascade may be quite high; in terms of temperature, some lo4 degrees. In the last step, this energy is dissipated by random atomic collisions until the temperature has fallen below the melting point, and subsequently the flow of phonons out of the cascade reduces further the temperature down to ambient temperatures. Finally, the relaxation of the atomic arrangement results in a stable defect pattern. The vacancies and interstitials that are produced by the displacement damage can interact in two ways. Vacancies and interstitials can be annihilated by recombination or by going to sinks such as the target surface, grain boundaries, etc. The other possibility is that the aggregates of vacancies or interstitials can nucleate and grow. Three basic morphologies of the clustering of point defects exist. Interstitials can aggregate into two-dimensional platelets or interstitials dislocation loops that can subsequently evolve into a dislocation network with increasing dose of ion bombardment. On the other hand, the vacancies that

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survive recombination can form either two-dimensional aggregates called vacancy loops or a three-dimensional empty space called a void. The void morphology is, however, formed at high irradiation temperature where both the vacancies and interstitials are highly mobile. (ii) The second type of damage is associated with impurity atoms introduced either by transmutation of the target nucleus or when the bombarding ions come to rest in the specimen. For example, helium impurities up to 30 at ”/, concentrations can be introduced into metals by tritium decay, (n, a) reactions, or direct a-implantations, Since the solubility of He in metals is less than a part per million, He tends to segregate in the form of small bubbles. In a fast reactor such a phenomenon plays a crucial role in degradation of material properties (Ullmaier and Schilling, 1980). In the displacement damage, the average number of displacements N, produced by an incident ion or an energetic recoil atom can be estimated from the knowledge of the deposited energy, r (E), not lost to electronic excitation, and the size of the displacement cascade, which is 10-1000 A for ions in the 1-100 keV energy range. The modified Kinchin and Pease (1955) collisional model gives Nd as (Sigmund, 1969b)

A necessary condition for the development of surface structure due to the displacement damage has been proposed by Hermanne (1973). During sputtering, if the surface that is continuously eroded approaches one of the extensive defects, e.g., dislocations, these cause a preferential erosion of the defect area with respect to neighbour zones. The consequent spatial variation of sputtering yield would then give rise to undulations at the surface (Hermanne and Art, 1970). Other regular surface features associated with the symmetry of the crystal, which may also develop, are the crystallographic etch pits and conical protrusions. The basic criterion for the possible appearance of the damaged-induced surface structure is that the time for formation of extensive defects must be less than the time for recession of the surface to their level, i.e.,

where d , is the depth of damage peak below the surface, v, is the velocity of surface recession by sputtering, dd is the distance between two neighbouring extensive defects, and u, is the average velocity of migration of defects. It is argued that the distance travelled on average by a point defect to an extensive defect is add.

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D. GHOSE AND S. B. KARMOHAPATRO

v, can be calculated directly from the sputtering yield S . d d is approximated by the mean projected range R , as calculated by Lindhard et al. (1963). The distance de depends on the number of extensive defects formed per unit volume, an estimate of which can be made on the basis of the Kinchin and Pease (1955) model of defect production and on the amount of point defects present at the concerned level. Thus, the minimum value for the migration velocity of defects is obtained (Hermanne, 1973),

where I is the ion dose rate, E ion energy, ro the radius of the defect, and IC a numerical constant. The criterion of whether radiation-damage-related surface structure appears or not thus depends on whether the defect migration velocity u, is larger or smaller than vmin given in Eq. (13). The value of urndepends primarily on the local temperature of the region where the migration takes place, but it is rather difficult to estimate reliably. It is recognized that the above theoretical treatment gives only an order-of-magnitude estimate of conditions under which surface structure will appear.

111. ION-INDUCED SURFACE MODIFICATIONS A . Cone

1. A Brief Review of the Works on Cone Formation Solid surfaces exposed to an energetic ion beam erode and frequently acquire well-defined topography. Cones, pyramids, pits, hillocks, steps, etc., have been observed, and there are evidences that they are closely related to the initial surface irregularities, impurities, intrinsic or ion-beam-induced defects, and variations in the sputtering yield as a function of the angle of ion beam incidence to the surface. The cones or pyramids are the most commonly recurring surface features produced by sputtering. Several review articles have appeared on this subject (NavinSek, 1972, 1976; Wilson, 1974, 1989; McCracken, 1975; Townsend et al., 1976; Carter et al., 1983, 1985a, 1987; Auciello and Kelly, 1984; Whitton, 1986). Giintherschiilze and Tollmien (1942) first reported and described the formation of submicroscopic cones on glow discharge cathodes of various polycrystalline materials. They found well-developed cones on Mg, Zn, Cd, Al, Sn, Pb, Sb, and Bi, and in some cases, they appeared on Cu and Ag, but

M O I l 1 t ~ ' l t . t )1iY f.'AS'T' ION B O M B A R D M E N T

83

surfaces of Au, Ni, Fe, and Pt were almost free of cones. The dimension of the cones increases during sputtering, and the cone apex angle is different for each metal. It was also observed that on some cathodes, cones were absent when the bombardments were made at higher temperatures. Later, Spivak er ~ 1 1 .(1953) described the cone development at high current densities on ion-etched a 1umi n i um. With the advent of the SEM with its three-dimensional capability, the interest in the field of surface ion-bonibnrdment effects has grown considerably. Stewart (1962) studied the formation of cones on ion-bombarded surfaces of Al, Si, W, and Sn with an early model of the SEM. He proposed that cones or spikes are caused either by inclusions or precipitates with a lower sputtering yield than the surrounding material, or by particles resting on the surface. When the shielding particle had been eroded away, a sharp spike or cone of matrix material remained. If the bombardment was continued, the spikes decreased in size and eventually disappeared. Similar behaviour has been reported for iron oxide particles on i r o n by Pease el uI. (1965)and for line dust particles of Al, Ag. or Si o n NaCl crystals by Marinkovii and NavinSek (1965). The shielding principle for cone forniation has been substantiated by the work of Wehner and Hajicck (1971). They found that cones formed when groups of low-sputter-yield atoms, M o or W, lay on the surface of high-yield material such as Cu, Ag, or ALLThe combinations such as C u - Ag or C u C, however. showed no sign of cone formation. They also noted the importance of solubility and activation energyfor migration of the low-yield atoms on the high-yield material. For low-yield carbon atoms seeded on a high-yield CLI substrate, cones d o not form under ion bombardment. When low-yield M o atoms replace the c' atoms, conical structures form. The M o a t o m not only protect the underlying C u from being sputtered, but also arc constantly replenished via surface migration. Wilson and Kidd (1971) studied the devclopment of cones on gold surfaces by 5 to 20 keV Ar' and Xe' ion bombardment. A high cone density was found to be characteristic of mechanically polished surfaces, whilst a low cone density with height contrast of the individual grains was discovered on polycrystalline etched surfaces. The cones were found to have hexagonal facets, and in the case of ii polycrystnlline specimen, two families of cones were found. These phenomena were attributed to single crystal effects. The cone angles were found t o vary only slowly with the ion energy. Similar bombardment of single crystals produced no cones, probably as a result of channeling of the incident ion beam. Conditions of cone formation on the sputtered surfaces of Cu, Ni. Mo, W, CdS and CdSe single crystals with respect to the ion dose, face orientation, and ion beam incidence angle were investigated by Gvosdover Pt 111. ( I 976). Intense

84

D. GHOSE AND S . B. KARMOHAPATRO

formation of cones was observed only when impure metal atoms were present on the sputtered surface. Such impurity either was a part of the target material or was sputtered from outside. As the ion irradiation dose increased, the cone heights and their surface density also increased. The cone density was, however, a function of crystallographic orientation of the sputtered face. This density appeared to be higher for less close-packed faces than for more closepacked ones. From the analysis of the data obtained, the authors concluded that the cone-like configurations appeared as a result of the three simultaneous processes of surface migration, growth, and sputtering. The main process responsible for cone formation was attributed to a growth process such that the sputtering in the course of ion bombardment shaped the cones into a form stable against sputtering. Recently, two groups, Whitton et al. (1977, 1978, 1980a; Whitton, 1986) and Auciello et al. (1979,1980; Kelly and Auciello, 1980; Auciello, 1982),made systematic investigations of the development of energetic ion-bombardmentinduced surface features on copper crystal, in which many interesting results were obtained. Whitton et al. (1977, 1978, 1980a; Whitton, 1986) bombarded superpure polycrystalline Cu by 40 keV Ar’ ions to a total dose of 1 x 10” ionslcm’ at room temperature. Cones were observed to develop on some grains but not on others, although all had the same conditions of bombardment. The individual grains were x-rayed to produce Laue patterns, the analyses of which showed that only of grains having orientation of, or near to, the high index direction of (11 3 1) were cones formed. Similar results were obtained for other f.c.c. metals (Whitton et al., 1984).The cones were later termed as pyramids since the observed features were of faceted shapes, having octagonal bases with triangular sides meeting at a point. For suitably oriented single crystalline targets, etch pits were always found to be the forerunners of pyramids. These observations led them to the conclusion that the mechanism of initiation of pyramid formation was associated with defects such as dislocations rather than impurities. The most critical parameter was that of crystal orientation. Pyramids were formed only of surfaces with orientations close to or of (11 3 1) crystallographic plane. Whitton et al. (1980a; Whitton, 1986) also suggested the following range of parameters within which pyramid-covered surfaces on (11 3 1) surfaces could be produced: total dose of 10’’ to 2 10” ions/cm’, temperature range 100-550 K, beam current > 100 pA/cm’, beam energy 10-41 keV, working pressure between 5 x and 5 x lo-’ mm of Hg. Auciello et al. (1979, 1980; Kelly and Auciello, 1980; Auciello, 1982) studied the morphological evolution of pyramids developed on polycrystalline Cu bombarded by 12 keV Kr’ ions as a function of ion doses. Their observations revealed that the initial surface topography was very important as far as the nucleation and development of pyramids were concerned. The presence of asperity or convex-up irregu-

-

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

85

larity on unbombarded surface was the prime factor for the development of pyramid. Such asperities can in principle be formed as a result of mechanical treatment, chemical treatment, inclusions, surface impurities, ionbombardment-induced damage associated with preferential erosion, or other causes, the precise details being unimportant. A one-to-one correlation was demonstrated between pre-existing asperities and pyramids. Sequential bombardments and SEM observations of the same features showed that pyramids are not an equilibrium structure. They disappear at high enough doses. The authors also obtained strong experimental evidence for the importance of secondary and tertiary effects in the evolution of pyramids, which involved scattered ions, reflected ions, and energetic sputtered atoms from the pyramids’ surface and the inclined walls of the grooves underlying the pyramids, respectively. Alexander et al. (1981) investigated the geometric relations between the orientation of the crystals, the faceted cones, and the sputtered spot patterns for Ag, Al, Au, and Pb single crystals with (1 11) surfaces bombarded with 13 keV Ar ions, not analyzed with respect to mass and charge. The crystals of approximately 1 mm thickness were cut from massive rods by means of a diamond wire saw and then cleaned by ion etching in a sputtering chamber. A scanning electron micrograph of the crystal surface cleaned in the above way showed high density of impurities on the surface. The impurities were either condensed cracking products produced during ion etching, or residues from the diamond saw. Intense cone formation was observed when the crystals were bombarded to a total dose of 2 10’’ ions/cm’. Different kinds of cones were found to develop on the bombarded surface-namely, cones with a small apex angle with or without impurities on top, cones with a small angle at the bottom but with a wider apex angle at the top, and completely faceted cones with a wider apex angle. The last type of cones exhibits a six-fold symmetry, ie., three main facets, each being structured into two subfacets. This type of symmetry is similar to that in the sputtered spot patterns. Electron channeling pattern studies showed that the bombarded surface remained single crystalline with the same structure and orientation as the original surface. Ghose et al. (1983a,b, 1984a) studied cone formation on various metals bombarded by Ar+ ions at different doses ranging from 1019to 10” ions/cm2. The metals were polycrystalline Cu and Ni and single cyrstals of Ag with faces parallel to (111) and (100) planes respectively. The results obtained from 30 keV 40Ar+-bombarded Ag single crystals seem to be quite interesting (Ghose et al., 1984a). These are: (a) The cone density is orientation-dependent; it is found to be lower on the (100) face than on the (1 11)face under the same dose of ion bombardment. Onderdelinden (1 968) showed that the sputtering yield S is considerably reduced along low index directions due to the channeling of ions. It is known that the cone is formed in such a way that its surface normal

86

D. CHOSE AND S. B. KARMOHAPATRO

makes an angle 0’ with the ion beam corresponding to the maximum sputtering yield in the angular dependence of the sputtering yield curve (see the following section). Since for an f.c.c. crystal (100) is a more close-packed direction than ( 1 1 l), the rate of erosion of the cones relative to that of the surrounding surface plane will be faster in the case of the (100) face than in the case of the (1 11) face. This implies that cones on the (100)face, if formed, would rapidly disappear with subsequent ion bombardment. Another possibility is that in the low index direction, the range of the ion is long, therefore the energy deposition and near-surface defect production rate are small, resulting in a lower probability of cone formation (Whitton et al., 1980a). (b) Cones are not an equilibrium structure consistent with the observations of Auciello et al. (1980; Auciello and Kelly, 1979). (c) In the latter stages of cone evolution the cones become faceted and pits develop at the bottom. The faceting indicates not only that the angle of ion incidence with respect to the local surface normal is important, but also that the orientation of the local crystal axis to the ion beam plays a significant role in the formation of cones. (d) At low doses of ion bombardment, grain boundaries develop and cones appear on some grains, while on others they are completely absent, as shown in Fig. 1. This is probably due to the fact that the polishing procedure tends to produce randomization of the surface grains that is revealed only at low ion doses where the erosion is small. This phenomenon did not occur when the crystals were bombarded with high ion doses. Finally, (e) a few cones on the (1 11) face are found to bend as shown in Fig. 2. There have been only a few reports of SEM observations of bent cones (Wilson et al., 1984).Belson and Wilson (1982) attributed the effect to bending under the stress associated with the surface tension.

2. Theoretical Considerations The most often proposed mechanisms, which relate to different experimental conditions, for the formation of cones on ion-bombarded solids are the following. In the first mechanism (Wehner and Hajicek, 1971; Stewart and Thompson, 1969), the plateau surface discontinuities caused by lowersputtering-yield impurities shielding the underlying material are modified into conical protrusions during erosion, as a result of the variation in sputtering yield with angle of ion beam incidence. The second mechanism (Gvosdover et al., 1976) is that the surface impurity is necessary for nucleation while the cone later grows by the interplay between sputtering and surface atom migration. Wehner (1985) recently has shown that the impurities need not have a lower sputtering yield as widely believed, but rather a higher melting point. The third mechanism (Whitton et al., 1977, 1978, 1980a) considers the initiation of surface discontinuities by intrinsic or ion-beam-induced defects followed by erosion to produce the final conical or pyramidal protuberance. A

FIG.1. Electron micrograph of the sputtered area of Ag(100) face after 1 x 10'' 30 keV Ar' ions/cm2. The viewing angle in the microscope is 33.5". (a) shows different cone densities on different grains; some grains are completely devoid of cones. White markers = 10 p n . (b) shows cones on one grain at high magnification. White markers = I pn. [After Chose et a/., 1984a.l

FIG 2. Bent cones on Ag(l1 I ) face bombarded by 30 keV Ar' ions to a dose of I x 10'' ions/cm2 The viewing angle in the microscope 15 3 3 5 White markers = I pm.

88

D. CHOSE AND S. B. KARMOHAPATRO

I

I

8'

0

I

so*

9-

FIG.3. Schematic diagram of the angular dependence of sputtering yield S(0).

fourth mechanism was advocated by Auciello et al. (1980; Kelly and Auciello, 1980; Auciello, 1982) where cones originate from pre-existing asperities on the surface combined with the erosion process caused by sputtering. In all the mechanisms of cone formation, the dependence of the sputtering yield on angle of ion incidence plays the major role. If 8 is the angle between the incident ion beam and the surface normal, then the sputtering yield S ( 8 ) follows a sec 8 law only over a limited range for small 8. At large values of 8, S ( 0 ) deviates from the sec 8 dependence, passes through a maximum at 8' between 60 and 80°, and falls towards zero at 8 = 90"as shown in Fig. 3. Such a variation is typical for amorphous and polycrystalline solids, while for single crystals the effect of channeling changes the curve significantly. In the following, the different theories of cone formation are described, where it is assumed that surface changes occur only as a result of atomic ejection, i.e., other processes such as surface diffusion, local variation of binding energy over a surface, and redeposition of sputtered material are ignored. Also, none of the theories take account of directional effects and they are, therefore, only applicable to isotropic materials. Belson and Wilson (1980,1981) have recently published calculations on contour changes of asperities by taking redeposition of atoms sputtered from the area adjacent to the feature into account. Chadderton (1979) has discussed the role of surface energy minimization in the development of the faceted cone or pyramid. a. The Theory of Stewart and Thompson Motion of the intersection between two plane surfaces due to ion-induced erosion was studied by Stewart and Thompson (1969). Figure 4 shows a surface consisting of two inclined planes A and B intersecting at 0.Angles of incidence of ions on the planes A and B are c( and p, respectively. Sputtering changes the positions of the planes

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

89

Ion Beam

FIG. 4. Motion of the intersectionbetween two plane surfaces during erosion. [By permission from Stewart and Thompson, Chapman and Hall,0 1969.1

to A‘ and B’ with the point of intersection moved to 0’.The angle 6 is defined as the angle between the direction of the incident ion and the line 00’.The distances a, b, c, and d are respectively defined as that advanced by the two planes A and B, by the point of intersection, and by the movement of the intersection transverse to the direction of incidence. Each of the planes is bombarded with the flux of ions CDcosa or CD cos 8, where Q, is the flux per unit area normal to the surface. It is evident from Fig. 4 and the geometry of the system that 1 a = -Q, cos as(‘%)= c cos(a

N

1 b = -CDcosps(p) N

+ 6) (14)

=

ccos(8 - 6),

where N is the density of atoms per unit volume. The ratio &a, i.e., the ratio of the distance due to transverse motion of the intersection and the distance of advancement of A, is

Three kinds of movement of the intersection can occur. (i) If S(a) = S(B), d = 0 and 00’does not move laterally; (ii) If S(a) > S(j), d < 0 and 00’moves towards B; (iii) If S(a) < S(B), d > 0 and 00’moves towards A.

Had the angle between A and B been acute instead of obtuse viewed from above as shown in Fig. 4, the direction of motion would have been reversed. In

90

D. CHOSE AND S . B. KARMOHAPATRO

FIG. 5. Evolution of a surface step under ion bombardment. [By permission from Stewart and Thompson, Chapman and Hall, 0 1969.1

conclusion, the crest of a ridge and the foot of a valley will move towards the side for which S(O) is least or greatest, respectively. Figure 5 shows the erosion of a surface step, where the profile 1 can be considered as an assembly of small planar facets such as 0,02on the convex part of the step and O,O, on the concave part of the surface. Applying the above criterion to the corners at O,, O,, 0,, and O,, one can deduce: (i) if 0 <

0, and 0, move to the right 0, and 0, move to the right;

(ii) if 0 > 0'

0, and 0, move to the left 0, and 0 , move to the left;

(iii) if 8 = 0'

0, moves to the left 0, moves to the right

I

and the facet grows;

0, moves to the right 0, moves to the left

I

and the facet shrinks.

Thus, the convex part of the step forms a facet with angle of incidence 0'. The concave part develops a smaller radius of curvature as the corners where 8 < 8' move towards to those for which 0 > O', thereby making a single concave corner. Finally, the profile 3 is obtained, where a single facet at 0' moves across the surface. Using the above results, Stewart and Thompson (1969) have proposed various stages in the formation of a conical structure as shown in Fig. 6. The experimental investigations of Witcomb (1974a) indicate that the cone development schematized in Fig. 6 is essentially correct. If a foreign particle, inclusion, or precipitate located on the surface is exposed to an ion beam, a

A-*-?i-

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

Impur ity. 2:riit-A-

91

FIG. 6 . Cone evolution according to the model of Stewart and Thompson (1969). [By permission from Stewart and Thompson, Chapman and Hall, 0 1969.1

step will first form under the edge of the particle. As the particle itself shrinks, the step will be inclined at an angle 8'. After removal of the shielding particle, the step further contracts inwards forming a cone of apex angle (n - 28') with its axis in the direction of ion incidence. At this stage, the cone tends to rapidly disappear since it erodes in the direction of the ion beam at a rate faster than the surrounding surface plane. b. The Theory of' Curter et al. Carter et al. (1971,1973; Nobes et ul., 1969) have analyzed the evolution of a line contour under ion bombardment when I ions/sec/unit length in the Ox direction bombard a surface in the - 0 y direction, in the plane xOy (Fig. 7). To determine the equilibrium configuration, one should consider the time variation of the spatial location of two points A and B on the surface generator y = f ( x , t ) at t = 0. A t A, the rate of bombardment per unit length of the generator is I cos 8 and the normal rate of recession of the surface is ( I I N ) S(8)cos8; here N is the number of atoms per unit area. The effective rate of recession in the Oy direction is thus

ay

I N

- _ = -S(8)-

at

'1

0

case = -IS ( 8 ) . coso

N

I o n Bomm

11111111

/y-f(x~O)

X

FIG. 7. Geometry of the evolution of a line contour under ion bombardment. [By permission from Nobes er al., Chapman and Hall, 0 1969.1

D. GHOSE AND S. B. KARMOHAPATRO

92

At B, the rate of recession in the Oy direction is -"Y at+ 6 x . g ) = ; s ( 0 + b t ( )

Subtracting Eqs. (16) and (17) and proceeding to the limit lead to the result 1 ay

a

I dS(0) 60 N d0 '6x'

a

Since the surface recedes only in the y direction, -(6x) at

= 0. Therefore,

I dS(0) d0 N d0 dx aY or, since tan 0 = -,

ax I dS(0) d0 a0 _ - _ _ cos2 0-

d0

N

at

dx

or, again, since S(0) is given approximately by S(0) sec 0 for small 0, a0 I d0 _ - - -S(O)sin0at

N

dx

(0 small).

These are equivalent expressions for the time evolution of the slope of the surface. In equilibrium, the slope of the surface does not change with time, i.e.,

a

-(ay/ax) = 0 for all X . It follows from Eq. (18a) at

I dS(0) d0 = 0. N d0 dx

If S is independent of 0, then either of the solutions of Eq. (19) predicts that a continuous contour of initial slope 0, will recede in the - y direction maintaining a constant slope. Since S is a function of 0, the surface topography changes during sputtering, except in the case of a plane surface. However, dS/d0 = 0 for 0 = 0, 0', and n/2,according to Fig. 3. Therefore, regions of curves initially at these slopes will remain unaltered. For angles other than the above, the change of slope can be followed from Fig. 8 showing a concavedownward surface bombarded in the Oy direction. 0 is initially greater and less

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

93

Sputtered contour after a short t i m e

I

A9 dx

I -V.

FIG. 8. Evolution of a concave-downward surface under ion bombardment. [By permission from hbbes etal., Chapman and Hall, 0 1969.1

d8 dS than 8' in the left and right portion of A respectively. For 6' > O', -, - and dx d8

a

eventually -(ay/ax) are negative. Hence the slope decreases until it reaches at

8 = 8'. Similarly in the 8 < 8' region dH/dx is negative, but dSld8 is positive,

a

so that -(ay/dx) is positive. Hence, the slope increases until the equilibrium at

condition is achieved, i.e., 0 = 8'. The equilibrium topography of a concave downwards curve thus becomes a straight line with a single slope of 8', the same conclusion obtained by Stewart and Thompson (1969). For a concave upward surface, similar arguments show that the equilibrium configuration would be a horizontal line, i.e., 6' = 0 if 0 initially is less than 8' all over the surface, but a vertical line, i.e., 6' N 7r/2 if 8 > 8'. Thus, in the case of a surface contaminated with material of low sputtering yield, a hillock will first develop at the site of each contaminant atom or atom cluster. The surface is then analogous to the concave downward surface of Fig. 8 and will degenerate with bombarding time into a cone of semivertical angle ( x / 2 - 8'). The above theoretical discussion on the changes of surface topography considers a two-dimensional surface. Smith et al. (1981; Smith and Walls, 1980)have proposed a three-dimensional theory of the development of surface topography during ion bombardment, which also includes the effects of surface crystallinity and the multiple stationary points evident in the angular dependence of the sputtering yield of monocrystalline solids.

94

D.CHOSE AND S. B. KARMOHAPATRO

A quite different approach based on the concept that a sputtered surface behaves as a wavefront in kinematic or nonlinear wave theory has been developed recently by Carter and Nobes (1984; Carter, 1986). It was recognized earlier (Carter et al., 1973) that Eq. (18b) had the form of propagating wave in the variable 8, but the effective wave velocity, instead of being constant, was varied with 8. Formalisms for the study of space-time developing wavefronts with nonconstant wave velocity have been developed. Solutions of the wave equation are used to determine the trajectories in space or characteristics that link positions on the surface at successive intervals of time. In geometrical optics, these characteristics have the meaning of optical rays. It was shown that the characteristic method could give important information about the development of edges, facets, and other surface gradient discontinuities.

c. The Theory of Barber et al. For isotropic solids there is a distinct similarity between chemical and ion-beam etching. Barber et al. (1973) realized this and applied Frank‘s kinematic theory of chemical dissolution of crystals (Frank, 1958, 1972) to sputter etching. Frank’s two theorems state: (i) The locus of an elemental area of crystal surface with a particular orientation is a straight line during etching (assuming that the etch rate is only a function of orientation). This line is termed a dissolution trajectory. (ii) The trajectory of this elemental area is parallel to the normal of the polar diagram of the reciprocal of the etch rate at the point of similar orientation (defining the etch rate as measured normal to the actual crystal surface). Before deducing the changes in surface topography during sputtering, Barber et al. (1973) plot the reciprocals of the sputtering ratio S(8)cosfl/S(O) on polar graph paper in accordance with the second theorem of Frank. This curve is called the erosion-slowness curve. Now taking a drawing of the surface of interest, they superimpose the erosion-slowness curve on it and draw the orientation trajectories parallel to the direction of the normals to the slowness curve at corresponding orientations. Finally, the depth eroded is measured along the direction of erosion at points along the surface using the known values of S(8). Thus, the new surface at any given time during bombardment is constructed, and this may be done at successive times to determine how the surface topography develops. The advantage of Barber et al.’s graphical method is that it can in principle be applied to a surface of arbitrary shape. But the shape of the S(8)-8 curve must be known before the evolution of surface topographies can be predicted in detail. d. The Theory of Sigmund Sigmund (1973) described a mechanism that can lead to microroughening of the surface. If an ion is incident non-normally

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

95

on a surface, since it has a finite range, the maximum sputtering effect will not occur at the very point of impact, but further “downstream”. This effect will lead to nonuniform sputtering rates. Applying his earlier sputtering theory (Sigmund, 1969a), Sigmund showed that on a length scale of the order of the penetration depth of the ions, a microscopically flat surface is unstable under high-dose ion bombardment, and cones or grooves develop from small irregularities. It is possible that atom migration could smooth out this effect, so that it should be temperature-dependent. Such hypothetical microscopic features are at the resolution limit of the SEM. Recent investigations of the cone apex region by TEM (Kubby and Siegel, 1986a,b) have shown evidence that supports the mechanism operating on the length scale of ion range. It has been asserted that this mechanism provides a link between the events taking place on an atomic scale and those features that can be predicted from the macroscopic variation of the sputtering yield with the direction of ion incidence. 3. Critical Doses of Cone Evolution

In all the models described above, the secondary and tertiary effects are not included. The secondary effect involves the scattered ions, reflected ions and energetic sputtered atoms from the surfaces of cones, while the tertiary effect involves the energetic sputtered atoms from the inclined grooves’ walls underlying the cones. These effects are very important in modifying the shape of the cones during evolution. More recently, Kelly and Auciello (1980) developed a model in which the effects of secondary and tertiary particles have been included, although in a semi-empirical form only. Kelly and Auciello (1980)considered the evolution of asperities of convexup curvature on an ion-bombarded surface (Fig. 9). Such asperities may initially be present on the surface, or they may originate from intrinsic or ionbeam-induced defects or impurities, the details of which are unimportant. The asperities interfere with the uniformity of sputtering process in two ways. (i) Primary effect: Owing to the existence of a maximum rate of sputtering, S(O’), for a particular large angle O‘, there is a tendency for the surfaces of convex-up features (Fig. 9a) to rotate until facets at angle 0‘ develop and the overall shape becomes conical (Fig. 9b). (ii) Secondary effect: Scattered ions, reflected ions and energetic sputtered atoms from the edges of cones can enhance the sputtering at the bottom. The potentiality for such effects is supported rather well by the work of Reid et al. (1976, 1980) in which experimental evidence is presented for the existence of a significant component of energetic (10- lo3 eV) sputtered atoms from surfaces that were bombarded obliquely. As a result, the cones tend to become better-defined and develop

96

D. GHOSE AND S. B. KARMOHAPATRO ION BEAM

Cb b b b b 4 bC b

+

deflected ions energetic target species C

energetic target {species

FIG. 9 . Schematic diagram showing different stages of cone evolution from a convex-up asperity under ion bombardment. (a) represents an asperity of height h , . This is convex-up at its center and passes through a slope 8‘ at some intermediate width g and height h. [After Auciello er al., 1980. By permission from Gordon and Breach Science Publishers Inc.]

grooves around them as depicted in Fig. 9c. In real systems, however, the shapes of 9b and 9c would develop concurrently. Now the tertiary effect consisting of energetic sputtered atoms from the groove walls comes into play. These particles hit the cones, producing enhanced erosion, which leads to enlargement of the apex angles (Fig. 9d) and their ultimate disappearance. Finally, the ever-enlarging pit remains, as shown in Fig. 9e. Using the formalism of Carter et al. (1971, 1973; Nobes et al., 1969) discussed in the previous section, Kelly and Auciello (1980) derived approximate expressions for the critical bombardment dose of cone formation and disappearance, which is described below: Considering the asperity shown in Fig. 9a, it is evident from the analysis in Section III.A.2 that the top of the asperity where 8 = 0 and the position with 8 = 8’ act as reference points of unchanging 8. For a fully conical shape to

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

97

come out, the following conditions should be met: K(8’)t + h , cot 8‘ = g

+ h, cot 8‘

(20a)

or

c K@’)

V,(O)l t

= h, 9

(20b) where q(8’) is the horizontal velocity of the real or extrapolated intersection of the position with 6 = 6’ and the substrate. The vertical velocity K(8) of a reference point is given by Eq. (16).The horizontal velocity VJ6) of a reference point is determined with the help of Eq. (16) as -

ax I K(6) = - = -S(8)cot 8. at N Since the intersection has both a vertical and horizontal component, it follows (Bayly, 1972) that

The critical dose for cone formation is now obtained from Eqs. (20a), (20b), and (21b) as the larger of ( I t ) , = 0,= N [ g tan 8’ - h ,

+ h2]/[S(8’)- S(O)]

(224

or (It), = 0 1 = N h z / [ S ( B ’ ) - S(O)],

(22b)

where O is the number of ions/cm2. In most cases, 8’ 65” and tan 8’ ‘v 2. Then it can be shown that Eq. (22a) corresponds to a “flat” asperity with 29 > h , , while Eq. (22b) corresponds to a “tall” one with 29 < h,. Both Eqs. (22a) and (22b), can be approximated as

-

2.

N h l / [ S ( O ’ ) - S(O)].

(224

For determination of the dose for disappearance of the cone, the following argument is considered. The vertical velocity of the center of a flat-topped asperity relative to that of the surrounding surface would be initially zero and would remain small until full conical shape is evolved. At this stage the relative vertical velocity would be K(0’) - K(O), and the condition that a cone of height h would disappear is

[V,(8’) - V,(O)]r ‘v h + j , (23) where j is the depth of the groove underlying the cone. Thus Eq. (23) includes the overall effect of secondary and tertiary particles. The total critical dose for cone existence O3can be considered as the sum of those for formation,

98

D. G H O S E AND S. B. KARMOHAPATRO

Eq. (22c), and disappearance given by

Q2,

derivable from Eq. (23). It is approximately

Q3 = N ( 2 h

+ j ) / [ S ( 8 ' ) - S(O)]

(244

or, assuming h = j , Q3 N

3 N h / [ S ( 8 ' ) - S(O)].

Kelly and Auciello (1980) found that the doses calculated with Eq. (24) are in reasonable agreement with the experimental values. 4. Cone Apex Angle From the theories of cone formation described in Section III.A.2, it appears that the variation of the sputtering yield with the angle of ion incidence plays an important role in the formation of surface cones, and the apex angle, a,, of such cones is given by the relationship a, = 180" - 28'.

(25)

The angle 8' is generally believed to be that critical angle beyond which the incoming ion has a probability of being reflected from the potential barrier presented by the surface atoms. As the value of (8 - 8') increases, both ion penetration and the sputter yield of the target rapidly decrease. Such a case of ion reflection can be considered somewhat analogous to channeling. Consequently, the theoretical analysis of directional effects in penetration of charged particles through crystal lattices by Lindhard (1965) lends itself to the problem. As 8' is generally in the range 60-80", it is assumed that the channel direction is very close to the surface. If t,b is the critical angle of channeling with respect to the target surface, then

8' = 900

- t,b.

(26)

Stewart and Thompson (1969) first determined the value of a, using Lindhard's theory of channeling. Later, Witcomb (1974b), generalizing their approach, described different methods of calculation to compute 8' and hence a,. In the following we discuss first the calculations of Witcomb (1974b) and then our own (Ghose, 1979). All the calculations that predict the cone apex angle are based on the same calculated planar potential from Lindhard (1965):

where N is the atomic density of the plane, y the distance of the ion from the plane, and V ( R )the ion-atom potential for separation R .

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

99

Using Lindhard’s standard atomic potential (Lindhard, 1965), Eq. (27) becomes Y(y)

=~

z Z , Z , ~ ’ N ~ ’ ~+[ 3u-f,)”’ (~’

-

y],

(28)

where uTF= 0.8853~,(2:’~ + Z:’3)-1’2.the Thomas-Fermi screening length. Thus in the surface plane, i.e., y = 0, the potential has a finite value, Y(0)

=

~ZZ,Z,~’N’’~&U~~.

(29)

From transverse energy and collision time considerations, the minimum distance of approach of an ion of energy E to a surface target atom is determined by the relation Y(0) = E sin’ t+h.

(30)

Equation (30) assumes that the deflection in the single collision is smaller than the total scattering angle. To a first approximation, $ can be written as

where e has been replaced by the Rydberg energy E, through the relation e’ = 2aoE,, and t,b is given in degrees. Since the continuous planar potential = Y(0)/2, we have from barrier of the plane is generally not nigher than Eqs. (26) and (31)

x,,

where 9‘ is in degrees, E in eV, and N in A units. This is essentially the expression quoted by Stewart and Thompson (1969),but with a square root in the denominator and a factor 347 instead of 443. The difference is due to use of an inverse-square form of the ion-atom potential (Thompson, 1969). At the lower-energy bombardment range, the barrier height becomes somewhat lower, and hence one would expect a somewhat smaller multiplication factor than 347 in Eq. (32). Since the extent of this reduction is not known, Eq. (32) is assumed to hold over the whole energy and atomic-number range, and the expression for the cone apex angle obtained from Eqs. (25) and (32) is

100

D. CHOSE AND S. B. KARMOHAPATRO

When compared with the experimental data collected by Witcomb (1974b), Eq. (33) gives satisfactory results only in the energy range between 20 and 30 keV. Below 20 keV the calculated values of a, are always greater than the measured values. The discrepancy between the theoretical and experimental values is also seen to increase rapidly with the decreasing value of Z2IZl. The second expression for a, can be obtained by a more rigorous solution of Eq. (27). If it is assumed that the incident particle happens to have a lattice atom directly below its orbit at the minimum approach distance, it can be shown (Lindhard, 1965) that the solution takes the form of

where i= ymin/fiaTFis a dimensionless parameter and E , = ( Z , Z 2 e 2 ) / (2n3&a&NZi3). Witcomb treats this basic inequality as an equality, substitutes the string expression rmin= d'$ for yminrand calculates values of $. The relevant solution of (34) is given by

Substituting the necessary values into the above equation yields the expression

To obtain a value for a,, Witcomb takes the value of d' as the closest packing distance between atoms in the string and finds that the cone apex angle can well be predicted by Eq. (36) in the energy range 0.2 to 30 keV for all types of incident ions and target elements. A further case is considered by Witcomb at very low energies, i.e., below 1 keV where the more appropriate interatomic potential is the Born-Mayer potential V(R) = A exp( - R/a,,), where A and aBMare usually determined phenomenologically, say by fitting the elastic moduli. In the surface plane, y = 0, the continuum planar potential (27) takes the form

:l

Y(0)= 2rtAN2I3 =2

R eXp( -R/a,,)dR

n ~ ~ * a;M. /3.

(37)

Applying Eq. (30) and assuming as previously that the effective potential Xff = Y(O)/2,it can be shown that ~

a, = 203[

~

2

'

]

3 112 ~

;

~

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

101

Using the values proposed by Andersen and Sigmund (1965) for A = 52(Z,Z2)314 eV and for aBM= 0.219 A, it is found that although Eq. (38) produces reasonable values at 1 keV, at other ion energies the calculated values are much inferior to those obtained from Eq. (36). From the above analysis of Witcomb, it appears that the cone apex angle can best be determined by Eq. (36). However, one should note that Witcomb’s expression contains two target lattice characteristics, namely, N , the number of atoms per unit volume, and d’, the distance between the atoms in a string. A fit with the experimental values is obtained by taking the d’ values as close-packed values. This can only be justified for single crystals where atoms are found to be ejected along low-index crystallographic directions. When a polycrystalline material is bombarded with energetic ions, no such preferential ejection of atoms occurs owing to the presence of grains of various orientations. Thus, it would be more appropriate to choose some form of statistical average atom spacing rather than the closest packing separation. It therefore seems questionable to use Witcomb’s relation with a randomly oriented target. In order to derive (Ghose, 1979) an expression for 8’, it is also important to choose an appropriate potential function. Published data reveal that for a certain projectile- target system, 8‘ varies slowly with projectile energy. This fact is also supported by Wilson and Kidd (1971),who obtained 8‘values from the measurement of the apex angle of cones developed on polycrystalline gold surfaces under argon and xenon ion bombardment at 5 to 20 keV. For this reason, they suggested that the interaction potential between the incoming ion and the target atom should be very sensitive to separation. One may, therefore, proceed with a power law potential function for the calculation of 8’. Onderdelinden (1968) used a R - 3 power potential in his theory of sputtering, which is suitable in the low-energy region. This potential has the form 3 ZlZ2e2a& V ( R )= (39) 2 R3 ’ The average planar potential corresponding to this interatomic potential is obtained from Eq. (27) as

In planar channeling, the projectile is steered by planes of lattice atoms. If one takes the mean separation of successive atoms in the plane along the projectile path as N - 1 / 3(Francken and Onderdelinden, 1970), then from the condition for continuum approximation one obtains (41)

102

D. CHOSE A N D S. B. KARMOHAPATRO TABLE I COMPARISON BETWEEN PREDICTED 0'. EQ. (42), OBSERVED

8'

VALUES OF OECHSNER

Projectile and target

E (keV)

@(theor) (degrees)

Ar+-AI Ar+-Ti Ar+-Ni He+-Cu Ne+-Cu Ar+-Cu Kr+-Cu Xe+,-Cu Xe+-Cu Xe+-Cu Xe+-Cu Ar+-Zr Ar+-Pd Ar+-Ag Ar+-Ta Ar+-Au

1.05 1.05 1.05 1.05 1.05 I .05 1.05 2.05 1.55 1.05 0.55 1.05 1.05 1.05 1.05 1.05

71.7 69.8 65.1 76.6 68.9 65.5 61.3 65 62.6 58.8 51.4 69.3 65 66.2 64.1 63.8

Substitution of the value of the expression

AND

(1973.1975)

B'(expt) (degrees) 70.5 70.5 71 71 70 61.5 65.5 70 65 60.5 56 68 60.5 61.5 65 58

II/ in Eq. (26) and further simplification yield

For illustration, the values obtained from Eq. (42) are compared with the results of Oechsner (1973, 1975) (Table I) and Evdokimov and Molchanov (1968) (Table 11). It is evident from Tables I and I1 that the agreement between calculated and measured 8' values is quite satisfactory at both low and high keV energies and also for different projectile- target systems. Thus, the approximation of the mean separation of lattice atoms with a suitable interaction potential can well replace the close-packed spacing d', which is actually not necessary for a polycrystalline target. In all the calculations described above, the angle 8' represents the critical angle for ion reflection. Chadderton (1977) has pointed out a mistake regarding the measurement of this angle. The resemblance between the ion reflection and channeling is more conspicuous when one studies the angular variation of sputtering yield normalized to the yield for normal ion incidence. The curve shows a characteristic shoulder as well as a characteristic trough (Fig. 10). While the former is caused by a process similar to quasichanneling,

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

103

TABLE I1 COMPARISON BETWEEN PREDICTED 0', Ey. (42). AND OBSERVED 0' VALUESOF EVDOKIMOV AND MOLCHANOV ( 1968) Projectile and target

E (keV)

O'( theor) (degrees)

Ne+-Ni Ar+-Ni Kr'-Ni Ar'-Cu Kr+-Cu Ne+-Mo Ar+-Mo Ne*-Ag Ar'-Ag Kr+-Ag

30 30 25 21 25 30 21 30 30 25

83 81.8 79.8 81.7 80 83.3 81.8 83.3 82.2 80.2

O'(expt) (degrees) 83 81 79 80 80 82 80 82.5 81 79

t * 1 S(0)

-

e'

0

e' so.

0-

FIG. 10. Schematic diagram of the angular dependence of normalized sputtering yield S(@/S(O). The "trough" is characterized by the critical angle 8". [After Chadderton, 1977. By permission from Gordon and Breach Science Publishers Inc.]

the latter is generated by ion reflection following correlated collisions with surface atoms. At the angle O', for which the maximum in the shoulder is reached, the ions penetrate and violently sputter the target, whereas at the angle t)", measured at half-minimum corresponding to the oneset of the trough, the ions are not able to surmount the potential barrier presented by the surface atoms. Hence the calculated value of O', although apparently agreeing with 8' (expt.), actually corresponds to the angle at half-minimum rather than the maximum in the shoulder. However, experimentally it is difficult to resolve

104

D. GHOSE AND S . B. KARMOHAPATRO

TABLE 111 COMPARISON BETWEEN PREDICTED ac, EQ. (43), AND OBSERVED a, VALUES OF WILSON AND KIDD(1971) FOR POLYCRYSTALLINE AIJ Bombarding ion type

E (keV)

a,(theor) (degrees)

aSexpt) (degrees)

Ar Ar Ar Xe

5 10 20 20

31.1 24.68 19.59 25.93

36.5 k 0.5 33.0 0.5 27.5 0.3 40+ 1 59k 1

+ +

the dilemma of whether the cone apex angle relates to the angle 8' or 8", as the errors in the measured values are relatively large compared to the small difference between the angles. The cone apex angle calculated from Eq. (42) is given by

Tables I11 and IV show the comparison between the predicted a, values from Eq. (43) and the observed a, values of Wilson and Kidd (1971) for Ar- and Xebombarded gold and of Tanovik et d. (1978) for Ar-bombarded copper. The latter one shows that the agreement between the two sets of values is reasonable. Some comments are required regarding the influence of various factors on the apex angle of cones. First, one must consider the effects of secondary and tertiary particles on the cone apex angle a,. As discussed in Section III.A.3,

TABLE IV COMPARISON BETWEEN PREDICTED a,, EQ. (43), AND OBSERVED a, VALUES OF TANOVIC ET AL. (1978) Ar+ + CU E (keV)

a,( theor) (degrees)

a,(expt) (degrees)

20 40 60 80

18.3 14.8 12.1 11.5

23 k 3 18k3 15 2 13k2

+

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

105

these particles tend to increase the value of a, with the increasing dose of ion bombardment. This is experimentally shown by Auciello and Kelly (1979) in the dose range -(6 x 10'' to 3 x lOI9 ions/cm2). Tanovic and Tanovic (1987), on the other hand, noted enlargement of cone apex angle only in a limited range of ion dose - ( 5 x 10'' to 2 x 10" ions/cm*). After reaching a certain maximum value, the apex angle decreases and finally maintains a certain stable value at higher ion doses k 7 x lOI9 ions/cm2. In the dose range 3.4 x 10l6 to 3.4 x 10'' ions/cm2, Nindi and Stulik (1988) observed an initial faster increase of the average apex angle before the angle levels off at doses greater than about 2.3 x 10'' ions/cm2. Other relevant factors that may change the position of the sputter-yield peak, O', and hence the value of ac,are the target temperature and the anisotropy of the collision cascades at low keV energies (Witcomb 1977a,b).Finally, it should be noted that though the cone apex angle is weakly dependent on ion energy, it has a much stronger dependence on the crystal orientation as observed for Cu (Tanovic, 1981)and Pb (Erlenwein, 1977) crystals. This is in conformity with the finding that in single crystals the final pyramid form is dictated largely by the crystallographic habit (Whitton et al., 1980a).

5. Experimental Techniques and an "Ideal Experiment "

Usually cones are formed by impurity contamination of the target surface during sputtering. In the absence of impurities, ion bombardment in properly chosen high index crystal directions can result in a high density of cone formation (Whitton et al., 1980a). Techniques to prepare surfaces with dense arrays of cones in low-gas-pressure plasmas created with RF, or in DC diode or DC triode discharges, were described by Wehner and Hajicek (1971; Wehner, 1985), Berg and Kominiak (1976), and Kelly and Auciello (1980). Rossnagel and Robinson (1982a; Robinson and Rossnagel, 1982) used a broad-beam high-intensity ion source such as a Kaufman ion source for impurity-induced sputter cone formation. It is noted that the temperature of the sample is critical for surface mobility of impurity atoms or adatoms, which is inevitable to initiate the formation of conical structures. Recently, Linders et al. (1986a,b) described the method of contamination lithography for the generation of microcones. The target surfaces are first provided with defined three-dimensional carbonaceous deposits at desired positions by electron-beam-induced contamination in an SEM, and then sputtered with 12.5-24 kV Ar' ions. The contamination process depends on beam size, current density, electron energy, residual gas composition, target surface condition, and temperature. For a great height-to-diameter ratio of the contaminant, a stationary focused electron beam is necessary, whereas a scanning

106

D. GHOSE AND S. B. KARMOHAPATRO

beam generates high-volume contaminants. For perpendicular ion incidence, microcones are obtained. For oblique incidence of 25" and target rotation around the surface normal it is possible to obtain cylindrical microstructures, and for irradiation under 45" with target rotation, one obtains double cone structures. Wilson (1974)and Naviniek (1976)described the conditions of an "ideal" ion bombardment experiment in which no surface features should develop. In such an experiment, the target should be a random one, ultrapure and with a smooth and homogeneous surface. No gas contamination of the surface from the environment is allowed. The ion beam should be magnetically analyzed, chemically inert, and normally incident on the target. When such conditions are fulfilled, one can decide what perturbation of the surface will be introduced in order to follow the development of cones in isolation from other effects. In real systems, however, the target surface tends to become more or less contaminated. Hence, a careful preparation of clean and smooth surface is necessary. The experiment should also be performed in an ultrahigh vacuum system ( p < lo-' torr). Whitton (1978) discussed the role of various factors related to the beam and target in the determination of depth profiles by sputtering. He showed that the beam impurity, changes in beam current, angular divergence of the beam, orientation effect of the target crystal, lattice defects, surface impurity, departure from the flatness of the surface, and bad vacuum in the target chamber-each of these tends to produce cones, pyramids, and etch pits, which often obliterate the underlying physics of the development of topography. One therefore demands a well-defined beam on a well-defined target in well-defined environments. Roberts (1963) and Verhoeven (1979) have reviewed different techniques to obtain atomically clean surfaces and their relative advantages and disadvantages. Before installation in an ultrahigh vacuum system, a pretreatment of the sample is required. After mechanical, chemical, or electropolishing and washing in alcohol, trichloroethylene, or acetone in an ultrasonic cleaner, the sample is finally cleaned in the vacuum system. There are several methods of cleaning: high-temperature heating, gas-solid surface reactions, sputter ion cleaning, electron-stimulated desorption, and cleaving. Even in high vacuum, one can maintain a dynamically clean surface, if the rate of removal of the atoms from the surface by sputtering exceeds the rate of contamination by the residual gases. In order to minimize the contamination of the target surface by foreign atoms sputtered from the beam-defining apertures, the final aperture is usually kept at a large distance, say 40 mm (Whitton et al., 1977), from the target. In addition, sometimes diaphragms made of the same materials as the targets are used (Auciello et al., 1980). Most of the experiments reported so far are a two-step process, i.e., one bombards the sample in the ion beam system to the specific dose level and then

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

107

transfers it to the electron microscope for observation. However, in order to follow the development of conical structures and the evolution with successive ion bombardment, i.e., for a quasidynamic investigation, in-situ bombardment and observation are required. Such an arrangement, i.e., an SEM with a builtin ion source, was first used by Stewart (1962), and later several such on-line systems have been reported (Stewart and Thompson, 1969; Weissmantel et al., 1974; Dhariwal and Fitch, 1977; Hauffe, 1978; Lewis et al., 1979, 1980a,b; Carter et al.,1984; Goto and Suzuki, 1988). Buger et al. (1978) used an SEM that was equipped with an energy-dispersive x-ray (EDX) spectrometer to detect the type of the impurity atom and its concentration at the top of the cones. Finally, it should be noted that in many experiments, development of any surface structure during ion bombardment is deleterious to the problem under study. Sample rocking and rotation are the techniques that are used to minimize the growth of unwanted topography when using ion beams to mill or thin samples (Lewis et al., 1986). The use of two static ion beams symmetrically inclined about the surface normal also partially alleviates the formation of ion-induced sputtering structures (Makh et al.,1982). Reactive ions such as N:, O:, and C1' sputtering, or a suitable choice of gas mixture, e.g., Ar/O, sputtering, are found to be beneficial for obtaining a comparatively smooth surface (Hofer and Liebl, 1975; Tsunoyama et al., 1974, 1976; Begemann et al.,1986; Katzschner er al., 1984).

B. Fuceting The term faceting includes various surface structures such as steps, terraces, furrows, channels, facets, pits, etc. The phenomenon of ionbombardment-induced reorientation of crystallites in thin films has also been discussed, by Auciello (1984b), in the context of faceting. The earlier works by a number of authors (Ogilvie, 1959; Haymann and Waldburger, 1962; Fluit and Datz, 1964; Cunningham and Ng-Yelim, 1969; Hermanne and Art, 1970; Elich et al., 1971) have shown that faceting during ion bombardment of single crystals is a general phenomenon. The {loo} and ( 1 1 1 ) faces of f.c.c. single crystals are generally most stable under ion bombardment (Ogilvie, 1959; Fluit and Datz, 1964; Chadderton et al., 1972; Lyon and Samorjai, 1967; Nelson and Mazey, 1967; Rhead, 1962). In addition to the thermodynamic stability of the crystal face, the focusing and channeling effect and the presence of reactive gases such as mercury and oxygen during ion bombardment seem to be principally linked to the development and enhancement of facets. Wehner (1958) presented an early evidence of characteristic etch-pattern formation in Ge bombarded by 100 eV Hg' ions. He observed pits having

108

D. CHOSE AND S. B. KARMOHAPATRO

FIG. 11. Pit formation in Ge after Ar' bombardment at adose > 10'' ions/cm*. The viewing angle in the microscope is 33.5". White markers = 10 pm (Ghose, 1982).

four-, three-, and two-fold symmetry on (loo), (1 1 l), and (1 10) surfaces respectively. Ghose (1982) observed regular pit formation in Ge by highenergy (20-30 keV) Ar' sputtering (Fig. 11). Symmetric pit formation, similar to that of Wehner (1958), in Cu single crystals was reported by Tanovic and Perovic (1976). Detailed examination of pit shapes revealed that pits are square or eight-angular on the (100) plane, triangular or six-angular on the (1 11) plane, and rectangular or trapezoidal on the (1 10) plane. The symmetry of these microrelief figures is strongly correlated with that of sputtering ejection patterns from the respective planes. The authors also noted that on well-polished and very clean single crystal samples, the surface relief structures were weakly expressed and uniformly distributed over the whole surface in accordance with the model of Hermanne and Art (1970; Hermanne, 1973). Ghose et al. (1984a) found that pits on 30 keV Ar+-bombarded Ag ( 1 11) crystal were conical and strongly faceted with a sixfold symmetry similar to that in the sputtered ejection pattern from the same face (Fig. 12). This similarity suggests that the alternate facets of the pits correspond to (110) planes, while the remaining facets are the (100) planes. According to the analysis of Smith et al. (1981), each of the facets of the pit corresponds to the direction of the minima of the angular dependence of the sputtering yield curve for a monocrystalline solid. Close inspection of Fig. 12 also reveals that the facets contain fine-scale ripples with a spacing of about 10,000 A. Similar background ripple morphology was found in major etch pit regions (Whitton et al., 1977), near protruding pyramids (Whitton et al., 1978; Stewart and Thompson, 1969) and also on the pyramid facets (Erlenwein, 1978). It is generally concluded that this is associated with elaboration of the subsurface

FIG. 12. (a-c) are electron micrographs showing faceted pits on the Ag(ll1) surface with a sixfold symmetry. (a) is after 5 x lo" 30 keV Art ions/cm2, and (b) and (c) after 3 x l O I 9 30 keV Ar' ions/cm*.The viewing angle in the microscope is 33.5".White markers = 1 pm. (d) shows the sputtered spot pattern from an Ar-bombarded Ag(l11) surface. [After Chose et al., 1984a.l

110

D. CHOSE AND S . B. KARMOHAPATRO

dislocation network that forms to relieve stress generated by ion-beaminduced defects. In the same experiment of Ghose et al. (1984a), it was also observed that when the bombarding ion dose is very high ( N 10" ions/cm2), terrace steps are developed. Fig. 13 shows typical terrace steps on an Ag(100) surface after 8.3 x 10'' ions/cm2. These are probably formed according to the mechanism proposed by Bayly (1972).When a curved surface is exposed to an ion beam, the rate of rotation of the surface tangent caused by sputtering is given by Eq. (18). Considering the enhancement of the particle flux at the foot of steep slopes due to scattered ions and energetic sputtered atoms, it can be shown (Bayly, 1972) that pits where the local slope initially exceeds 8' will develop with bombarding time into steps of 90" walls and 0" bases. In many sputtering experiments, polycrystalline targets are used. When such a target is bombarded by energetic ions, there will be a differential sputtering due to the presence of individual grains. As a result, a stepped surface topography usually develops, as shown by Tortorelli and Altstetter (1980) in Ar+-bombarded Nb (Fig. 14). Sometimes surface structures may develop on some grains, while other grains remain completely unaffected (Mazey et al., 1968).

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

111

FIG. 13. Electron micrograph showing terrace steps on an Ag( 100)surface after 8.3 x 30 keV Ar' ions/cm2.The viewing angle in the microscope is 33.5". White markers = 10 pm, [After Ghose et al., 1984a.1

FIG. 14. Electron micrograph of a polycrystalline Nb surface sputtered with 7 x 10" 15 keV Ar' ions/cmz.The angle of ion incidence is 22'. [After Tortorelli and Altstetter, 1980. By permission from Gordon and Breach Science Publishers Inc.]

1. InJuence of Facering o n Sputtering

Solid surfaces subject to energetic particle bombardment generally develop characteristic surface structures due to sputtering. Once the structures grow, on subsequent bombardment they must give rise to changes in the integral and differential sputtering yield from that of a flat surface. This is the consequence of two competing effects: a yield increase by an enhanced

112

D. GHOSE AND S. B. KARMOHAPATRO

effective projectile incidence angle, and a yield reduction by recapture of obliquely ejected particles by the protruding elements of the structure. Gurmin et al. (1969) first calculated the effect of surface structures on sputtering yield and showed that even heavily structured surfaces reflect the same emission distribution from a flat surface. Their conclusion that the topography has no influence on the differential yield was drawn because some special cases were generalized that had been taken as representative of the phenomenon as a whole. The analytical calculations of Littmark and Hofer (1978), on the other hand, show that surface structure exerts a profound influence on the sputtering yield. The calculation is based on the following assumptions: (i) The surface structures are stable under the chosen irradiation conditions. That means the facet angles remain unaltered during bombardment, though the individual facet may move across the surface. (ii) The facet planes are large enough so that edge effectscan be neglected. (iii) Only the ascending branch of the yield vs. incidence angle curve, which extends from zero to about 70"(see Fig. 3), is included in the calculation. This means that reflection of projectiles from facet planes, and therefore enhanced sputtering from facet bottoms, is neglected.

In Fig. 15 the faceted surface is characterized by the facet planes A and B, which are inclined at the angles tl and /Ito the nominal (macroscopic) surface plane of the crystal. A polar coordinate system is constructed on each of these three planes where the surface normals are the polar axes and the plane of symmetry of the facets is the azimuthal reference plane. B indicates the direction of bombardment or the direction of observation, as the case may be. All quantities related to facets A or B are indicated by the respective superscripts, while those referring to the nominal surface have no index. The

FIG. 15. Definition of structure parameters, coordinatesystems, and reference planes. [By permission from Littmark and Hofer, Chapman and Hall, 0 1978.1

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

kton c,'

h.cota

'

113

h.cotp

FIG. 16. Characterization of the variables E and x , shadowing limit E(x), and beam partition. [By permission from Littmark and Hofer, Chapman and Hall, 0 1978.1

relation between 8* or OB and 8 is given by cos BA = cos 8 cos a - sin 8 sin LY cos cp cos ON = cos 8 cos p

+ sin 6 sin fl cos cp.

(44)

The shadowing effect, i.e., the recapture of sputtered particles by the neighbouring facet plane, can be understood in Fig. 16, which is the projection of Fig. 15 on the symmetry plane for the facets. The angle that the direction of bombardment or the direction of sputtering emission makes with the nominal surface normal is denoted here by E. E is connected to the polar coordinates by tan(a - E ) = tan BA cos rpA

- cos 8 sin a + sin 8 cos LY cos cp

cos 8 cos a - sin 8 sin a cos rp

tan@

+

E)

= tan dBcos cpR

- cos 8 sin p - sin 8 cos p cos cp

(45)

c o s B c o s ~+ sin8sinpcoscp'

The directional region where sputtered material from part of plane A is shadowed by plane B is n c0 > - - p

or

2

-1

< cos cp, < - cot pcot O0

(case I). (46)

Similarly, the directional region of shadowing by plane A is E,

n

< a -2

or

cot a cot 8, < cos cpo < 1

(case 111),

(47)

114

D. GHOSE AND S. B. KARMOHAPATRO

and the region where sputtering emission is not hindered is 71

71 C ( - - < E , < - - ~

2

or

2

-cotpcot8,
(caseII). (48)

The differential sputtering yield dS(Fi,Fo)/dR, is defined as the number of particles emitted per solid angle element dQo around eo per projectile impinging on the surface from direction Fi. Provided that the shape of the emission distribution for a flat surface is not dependent on the projectile incidence angle, the differential yield from a flat surface can be written as dS(Fi,e,) = fi(Fi)f,(F,) dRo = fi(C0s ei)jo(coseo)m,.

(49)

In Eq. (49) it is further assumed that the emission distribution has no azimuthal dependence, which is quite reasonable for amorphous and polycrystalline targets and even for single crystals where random emission always dominates preferential emission. Now, the sputtering from a faceted surface can be calculated as the linear superposition of the sputtering from the A and B planes separately, taking into account the shadowing effects. After some trigonometric calculations it can be shown that

--

-

dQ0

I

cos 8B + f i ( C 0 S e;)---fo(cos cos ei COS e; er)--f0(~~~ e:)cOS ei

~~(COS

0:) cos 6, cOS

e:

sin u sin(u 8)

+

case 11, and

case 111.

From Eq. (50) the total yield S is obtained by integration over the whole free space of emission, i.e., c1 - 1 < E, 1- B. To perform the integration one must know the form of emission distribution function. Experimentally it is found (Vossen, 1974; Oechsner, 1975) that for polycrystalline targets under perpendicular ion bombardment, particle ejection occurs symmetrically to the target normal, changing from an undercosine distribution at bombarding energies of some 100 eV to an overcosine shape at energies above some keV. Emmoth and Braun (1977) have

-=

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT

1 15

shown that the angular distribution function can be fitted to a sum of a c1 cos 0 and a c2 cos20 term, where c1 and c2 are arbitrary constants but depend on bombarding energy and ion-target combinations. Accordingly, Littmark and Hofer (1978) considered a power form of fo, fo(cos 0,) = (COS OO)mo,

m, = 1,2.

From these two terms one may construct undercosine as well as overcosine distributions. The incoming projectile flux distribution is of the form fi(c0~ ei) = ci(cose i ) m l ,

mi < 0,

(52)

where ci is a constant depending on energy and the type of ion and target. Since only the ascending branch of fi(cos Oi) is considered, the relation based on Eq. (52)is limited to Of,0; ,< 70". Inserting Eqs. (51) and (52) in (50),one can obtain the explicit expression for the differential yield, and by integration the total yield. Several interesting conclusions can be drawn by examining Eq. (50) for various combinations of rn, and mi as discussed in detail by Littmark and Hofer (1978). For most of the experimental data at medium to high projectile energy, mo = 1, which gives > 1 for mi < - 1. Since mi usually lies between - 1 and - 2, the results SA+B/S show that the yield from a faceted surface always exceeds the yield from a flat surface. Furthermore, provided the projection of the beam on the nominal surface does not coincide with the line of intersection of the facet planes, it can be shown that there are remarkable distortions in the shape of the emission distributions caused by the influence of faceting when the projection of the direction of observation on the nominal surface is away from the line of intersection of the facet planes, particularly along the line normal to it. The inferences drawn for a faceted surface topography are equally pertain to cone/pyramid-covered surface. The relative importance of yield enhancement due to oblique ion incidence at the cone surface and the yield reduction due to shadowing by the neighbouring forest of cones obviously depends on a number of factors-namely, crystallographic structures of the cones, cone heights, cone apex angles, and the density of cones over the surface, the overall effect of which is reflected in the emission distribution and the total yield. Thus, Whitton et al. (1980b) observed -50% greater overall sputtering yield from the pyramid-covered (11 3 1) Cu surface than from the flat surface of the same orientation. Besocke et al. (1982) also reported similar results in the case of Ag sputtering. Mattox and Sharp (1979),on the other hand, found 30-40% lower yield in the case of needle-like cone morphology, indicating the prevalence of the recapture of released sputtered particles. Kundu et al. (1985) have measured the angular distribution of sputtered Ag particles at high-ion-dose-induced sputtering where conical protrusions

116

FIG.17. (a) Angular distribution of sputtered Ag atoms after 7 x 10" 30 keV Ne+ ions/cmz bombardment, the angle of ion incidence being40". Curve I shows thedistribution in the plane of incidence, and curve I1 in the plane perpendicular to it. Open circles are the experimental points, while the solid curves through the data points show the trend of experimental variation. (b) Scanning electron micrograph of the sputtered Ag surface showing cones. The ions are incident from the right. The viewing angle in the microscope is 0".White markers = 1 pm. [After Kundu et a/., 1985.1

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are formed at the surface. The angular distribution is found to be symmetric with respect to the surface normal, and overcosine at normal angle of ion incidence, whereas at an oblique angle of ion incidence, the distribution is asymmetric in the plane of incidence and symmetric in the orthogonal plane. Fig. 17 shows a typical angular distribution curve for 30 keV Ne' bombardment at oblique incidence of 40°, and the corresponding electron micrograph of the Ag surface. The cones are seen to be aligned along the direction of the beam. The results can be understood qualitatively from the above analysis of Littmark and Hofer (1978). Yamada et al. (1979) also estimated surface microstructural effects on the angular distribution and showed that the grain size has an influence both on the surface topographic changes and the angular distributions. 2. Surface Modijications in Semiconductors Semiconductor materials have wide applications in the microelectronics industry-the trend of which is towards the fabrication of integrated circuits with increasingly high density and devices with progressively smaller features (Lee, 1979). Microelectronic circuit fabrication is based on the ability to remove and add material selectively from and to the surface of a suitable substrate. At present wet chemical, plasma and sputtering methods are used to etch the required structures. To sputter-etch the target material, an ion beam etching or ion milling technique is utilized in which bombardment is by lowenergy ions such as Ar'. This technique has several advantages. Firstly, ion beams can be used to etch any material, even those with a multilayer structure that might be difficult using wet chemical etching and other dry etching techniques. Secondly, its high controllability allows the generation of patterns down to submicrometer dimensions (Melliar-Smith, 1976; Somekh and Casey, 1977). Since the geometrical and electronic properties of etched surfaces affect device characteristics, it is important to study the damage and topography generated by ion bombardment. Low-energy ion bombardment also has important application in the analysis of electronic materials, such as by secondary ion mass spectrometry (SIMS). Inert-gas or reactive-gas ions are used as primary excitation agent in SIMS to obtain the depth distribution of dopants and contaminants in semiconductors. The development of any topography during bombardment may constitute resolution limitations in depth profiling. Thus care should be taken in the choice of primary ions and also the dose for minimizing topography development. In semiconductor technology, Si is most widely used material because silicon devices exhibit much lower leakage currents. Recently, compound semiconductor technology has got attention for having electrical and optical properties that are absent in silicon. These semiconductors, e.g., GaAs and InP, are used mainly for microwave and photonic applications.

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Wilson (1973) pioneered the systematic investigation of the topography of a number of semiconductors after 40 keV Ar' bombardment. Si, Ge, GaAs. and InP exhibit relief structures in the form of undulating surface and narrowangled cones, which, however, can be removed by continued sputtering. Such a behaviour is consistent with an amorphous surface. The other group of materials studied, namely, CdTe, CdS, and Gap, are found to retain their crystal structure at the surface after sputtering, and the topography developed depends sensitively on the beam orientation. In the case of InSb, the surface appears to undergo a chemical change and tall whiskers grow from the indium-rich areas. Among the semiconductor materials, Si is the most widely studied element both by inert-gas ions such as Ar' and reactive-gas ions such as 0; and Cs' ions. The group of Carter et al. (1977, l982,1984,1985b,c;Lewis et al., 1980b; Begemann et al., 1986) studied extensively inert-gas irradiation-induced topographic changes of Si. The surface morphology development critically depends upon ion fluence or depth eroded. In the fluence range 1019lo'' ionsjcm', following an initial period of the production and expansion of individual etch pits, these overlap to form a terraced or corrugated ripple structure, the amplitude and wavelength of which increase with increasing ion fluence and mean eroded depth. A sequence of micrographs of Ar+-sputtered Si surface with ions incident at 45" to the surface normal is shown in Fig. 18 to exemplify this behaviour, as a function of increasing ion fluence. The ripple habit alignment lies transverse to the projection of the ion flux on the surface plane. For 70"to normal incidence a corrugated appearance also persists, but habit alignment is now parallel to the surface projection of the flux. At normal incidence, however, there are only few etch pits and the surface appears relatively plane. It was further noted (Lewis et al., 1986) that surface terracing or rippling no longer occurs over the mean sputtered surface under sample rocking and rotation or distributed ion flux conditions. Surface topography minimization also occurs if the surface is pre-irradiated at low ion fluence (Carter et al., 1984). For 0' irradiation no clearly definable microscopic morphological evolution was obtained up to fluences of lo'' ions/cm' (Carter et al., 1984). The results are consistent with those of Tsunoyama et al. (1980) for 20 keV 0; + Si at a dose of 3.2 x lOI9 ions/cm2 as well as for Ge to a dose of 1.4 x 1019 ionsjcm'. A tentative explanation for the observed surface features was given by Carter et al. (1984). For inert-gas ion bombardment, it is thought that stresses are developed parallel to the surface between the surface zone in which collision-induced recoils are generated and the underlying substrate. This initiates microcracks, the precursors of pits that ultimately evolve into corrugated structures. For oxygen irradiation, because of the comparatively high binding energy of the oxygen atom to the target atom (8.3 eV) (Tsunoyama et al., 1980), a near-surface silicon oxide layer is formed, N

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I19

FIG. 18. Corrugated surface structure developed upon Si by 7 keV Ar+ ion bombardment at 45’ incidence to the surface normal. The sequence (a)-(d) shows the increase in amplitudeand wavelength of surface facets as a function of increasing ion fluence: (a) fluence = 2 x 10l8ions/cm’; (b) fluence = 1.6 x 10’’ ions/cmz;(c) fluence I6 X 10’’ ions/cm2,and (d) fluence = 8 x 10” ions/cm’. The magnification of all the micrographs is 5000 X . [Reprinted by permission from Vacuum 34, Carter, G., “Some problems and prospects in high erosion yield sputtering.” Copyright 0 1984, Pergamon Press PLC.]

which relieves the stresses developed, and hence pits and subsequent development of topography are inhibited. It may be mentioned that cone formation in Si is rare unless large contaminants or asperities are present on the surface (Wilson, 1973; Morishita et a/., 1988). Duncan et al. (1983, 1984) systematically studied the effects of 5.5 keV ion bombardment on some important electronic materials such as Si( 100), Crdoped semi-insulating GaAs(100), and Fe-doped InP( 100). The primary ion species used are 0;and Cs’ since these enhance the electropositive and

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D. GHOSE AND S. B. KARMOHAPATRO

electronegative ion yields, respectively, in SIMS analysis. Relatively high doses of 1019 ions/cm2 to lozoions/cm2 have been used to ensure that the observed features are properly developed. In general, the microtopography observed to occur in all three materials with 0 ; bombardment is a stepped and faceted structure somewhat resembling that observed with inert-gas ion bombardment in Si (Carter et al., 1984).The structure is found to be better defined on Si(100) and InP(100) than on GaAs(100). In each case, the pitch and the magnitude of the morphological features increase with the depth of erosion. In passing, it may be mentioned that for Si, Carter et al. (1984) observed almost featureless surface after bombardment of 7 keV 0' ion. Duncan et al. (1983), however, noted that if the bombarding 0 ; energy is increased (10 keV), the Si surface remains almost featureless except for the occurrence of occasional faceted pits. Since the sputtering yield for a diatomic molecule at 2E is approximately twice the yield for the corresponding atomic ion at E (Andersen and Bay, 1981), the differences in the depth of erosion and the implanted oxygen concentration may be responsible for the difference of topography in the two cases. In contrast to 0 ; bombardment, Cs' bombardment has been shown to produce an overall smoother surface on Si(100)and GaAs(100) both at comparable ion doses and, more particularly, at comparable erosion depths. However, at a very high dose of lo2' ions/cm2, ripple topography begins to appear in the GaAs(100) surface. In contrast, Cs+-bombarded InP(l00) surface shows a complete different topography, which is cones appearing singly or in groups. The cones are first observed at relatively low doses (10" ions/cm2), and their size and density increase with increasing dose. The cause of cone formation is presumably the presence of predoped highmelting Fe impurity (Wehner, 1985) and the preferential sputtering of the P-component. Quite recently, Stevie et al. (1988) studied the correlation of changes in secondary ion yields to changes in topography during 0 ; and Cs+ ion bombardment of Si and GaAs crystals. For 0 ; bombardment of Si, the onset of ripple topography is indicated by a 68% increase of 28Si+ion yield, which occurs around a depth of 3 pm. For GaAs, change of ion yield was found over a depth interval of 0.3 to 1 pm, where the surface topography changes from a very lightly rippled to a furrowed structure. Neither change in ion yield nor surface topography occurs for Cs+ bombardment over a depth of 9 pm in Si and 1.9 pm in GaAs. Homma et al. (1985) found the development of small rounded protrusions of -0.1 pm dimension on the surfaces of Cs+-bombarded Si(lOO), GaAs(100), and InP(100). The bombardment was made in a SIMS instrument. The doses were not high enough to produce ripple topography. 0; and Ar+ bombardment also show similar microtopographies only in InP. It is thought that the formation of an altered layer by preferential sputtering of the high-

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vapor-pressure component in compound semiconductors, especially in InP, plays an important role in the development of topography. Cone formation on InP crystal was reported by Linders et al. (1986~)for Ar' and 0;ions sputtering in the energy range 3-10 keV. Three types of microstructures occurred during ion bombardment: contamination-induced surface roughness, densely standing cones of height and mean distance 5 to 25 pm, and regions of closely packed small cones of height and mean distance 0.2 pm. X-ray microanalysis reveals that sputtered Ta impurities from the beam-defining diaphragm are responsible for cone formation. It is interesting to note that the formation of a small cone region can be prevented by air exposure after irradiation with low ion doses. Such regions can also be eliminated when etched by a mixture of 75% Ar and 25% 0, ions (Katzschner et al., 1984). Wada (1984) bombarded InP crystals with 500eV Ar ions at normal incidence from a Kaufman ion source. Following the formation of small globules, sharp cones of 9.5" half-angle were obtained after prolonged irradiation. Auger analysis of the etched surface shows P deficiency and In accumulation in the surface layer of about 150 A thickness. It is theorized that these In atoms form minute globules and possibly act as nuclei for formation of sharp cones. When the bombardment is made at glancing angle, a nearly stoichiometric planar surface morphology is obtained. Topographical changes in the surfaces of GaAs( 100)crystal produced by 30 keV Ar' beam sputtering at various temperatures were studied by Bhattacharya et al. (1987). It was found that the bombarded surface remains almost featureless except for the formation of a few isolated pits for samples that were not externally heated (Fig. 19)and a few isolated conical protrusions

FIG. 19. Electron micrograph of a pit on a GaAs( 100)surface sputtered with 1 x 10'' 30 keV Ar+ ions/cm2. The viewing angle in the microscope is 0". White markers = 1 pm. [After Bhattacharya et a/.,1987.1

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D. CHOSE AND S. B. KARMOHAPATRO

FIG.20. A cone formed on a CaAs(100) surface sputtered with 1 x l O I 9 30 keV Ar+ ions/cm2; target temperature = 225°C. The viewing angle in the microscope is 33.5”. White markers = 1 pm. [After Bhattacharya ef al., 1987.1

for samples bombarded at high temperatures (Fig. 20). However, one observed a high density of cones when the sample was bombarded with simultaneous seeding with Cu at high temperature. It is thought that high-melting-point CuO is responsible for such cone formation (Wehner, 1985). In a compound target, the elements contained may also serve as seed material for cone formation. This may happen by preferential sputtering of one component and surface diffusion and clustering of the other component. The stoichiometry of GaAs was found to be unchanged during bombardment; this might be the reason for the absence of cones without the introduction of foreign atoms.

3. Colour Changes in Ion-Bombardment-Induced Textured Targets An ion-induced textured target often exhibits different colour when light falls on it. Depending upon the size and spacings of the microstructures, the topography may act as a total photon sink, sometimes selectively absorbs lights of particular wavelengths, and sometimes causes total reflection in a particular direction. The colour of the bombarded surface is found to be dependent on the direction of observation since metallic reflection also plays a role in it (Jenkins and White, 1957). In an early study of Si bombardment, Nelson and Mazey (1968) observed colour changes on the bombarded part with increasing ion dose. Faint blue or pink hues are observed initially which eventually saturate into a characteristic “milky white” appearance as the dose builds up. It is thought that Rayleigh scattering of the incident white light by the ion-induced disorder zones is

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responsible for such colour changes. Similar “milky spot” was also observed by Elich et al. (1971)in a Cu(100) crystal turned around a (100) axis when the incident ion beam made an angle of 39” with the surface normal. A replica of the bombarded surface in an electron microscope shows the presence of faceted surface structures, the width of which has the order of magnitude of the wavelength of visible light. A number of authors (Wehner and Hajicek, 1971; Kerkdijk and Kelly, 1978; Mattox and Sharp, 1979; Linders et al., 1986c) observed that closely spaced cone-covered surfaces of various solids, e.g., Cu, Mg, Be, and InP, are optically very absorptive and appear black when viewed perpendicular to the surface. The mean height and relative separation of such cones are 0.20.5 pm. Whitton et a/. (1978), however, observed selective absorption of light where only red light is reflected in a pyramid-covered (1 1 3 1) Cu surface. The pyramid apex angle is presumed to cause such selective absorption, which, in turn, should be projectile energy-dependent. The possible use of ion-bombardment-induced textured surface as a “solar absorber” was investigated by Berg and Kominiak (1976) and Rossnagel and Robinson (1982b).The selective absorption of light and low optical reflectance are thought to be due to multiple reflection between the facets of the structures, which are on the same physical scale as the wavelength of light. Dendritic needlelike structures on a tungsten surface formed by chemical vapour deposition (CVD) also show similar properties (Cuomo et al., 1975; DiStefano et a/., 1979). DiStefano et al. (1979) described a geometric optical model in which light is decomposed into components of multiply scattered light according to the order or the number of reflections it has undergone, as shown in Fig. 21. The total reflectance &( 0), for I, light incident on the surface at an angle 8 is

where the nth component is due to light of wavelength A that has been reflected n times from the facets of the surface structure. The coefficients a,(0) represent the fraction of rays that are scattered n times before escape, with X u n = 1. R(A,8)is the reflectance for light incident at an angle 0 on a smooth surface. At most wavelengths, second-order reflection is found to dominate the reflectance up to 8 60°, beyond which the first-order reflection becomes important. The model can predict the reflectance of a textured surface once the parameters characterizing the surface geometry are known. Though the model is applicable for light of wavelengths appreciably smaller than the dendrite spacing, it is approximately correct for wavelengths larger than the spacing.

-

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FIG.21, Schematic representation of a dendritic-tungsten surface obtained by CVD. The first-, second-, and third-order reflections of incident light are indicated. [After DiStefano et al., 1979.1

C . Blistering 1. Introduction

Blistering is the name used to describe the surface deformation caused by insoluble gas ion implantation in solid materials. The main criterion for this type of surface deformation is that the implanted gas profile must have a peak at least 10 nm below the surface. This is usually achieved by light ions, e.g., H + or He+ with E > 1 keV. Such low-energy light ions also have very low sputtering yields S << 1; consequently, the small erosion due to sputtering does not release the previously implanted gas. Further conditions are that the loss

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of gas due to diffusion, thermal desorption, and ion-induced reemission must be small. Although blistering was observed as early as 1912 by Stark and Wendt (1912), the first detailed analysis of blistering phenomena was made by Primak (1963; Primak and Luthra, 1966).In this work blister heights, diameters, shell thickness, and depth of cavities left after exfoliation were measured for both He' and H + bombardment of corundum and other minerals, magnesium oxide, Cu, and Ni. He also developed a quantitative model of blister formation associated with coalescence of small bubbles. Kaminsky (1964) first reported mass spectrometric observations of gas bursts released from ruptured blisters. Since then a lot of work has been done in this field, as can be seen in the review work of Das and Kaminsky (1976) and more recently in the work of Scherzer (1983, 1986). Readers are also referred to the blistering section of the proceedings of the international conferences on "Plasma Surface Interactions in Controlled Fusion Devices", all published in J . Nucl. Muter. (1974, 1976, 1978, 1980, 1982). Scherzer (1983, 1986) gave an account of keV-energy He-trapping and surface modification in different dose ranges. Initially, He doses of 10'4-10'7 ions/cm2 create damage in the form of point defects sufficient in number to trap all migrating heliums. Dislocations quickly grow into loops, after which a dislocation tangle is formed and small gas bubbles appear. No modifications of the surface structure are observed, but the bombarded surface expands outward due to swelling. Upon further implantation (21 10'7-10'8 ions/cm2), the peak helium concentration continues to build up until saturation is reached. At this stage the implanted helium starts to be reemitted, and at the same time the surface is deformed by blistering or flaking. Proceeding to very high implantation doses ( > 1OI8 ions/cm2), a repetition of blistering and flaking may occur. They are eventually eroded away by sputtering, and the final surface structure resembles that due to sputtering. At this stage, no further generation of blistering is possible because the helium-saturated layer is now exposed to the surface, and the condition that the peak should lie at some distance from the surface is no longer satisfied. 2. Factors Aflecting Blister Formation Mezey et al. (1982, 1987) have given the following classifications of morphologies due to He bombardment to avoid some confusion in the terminology. (i) Blistering: This formation dominates in the low-energy region ( N _ 1 keV- 1 MeV).

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(ii) Exfoliation: This is a large formation similar in shape to blistering but covering almost the whole implanted spot. This formation usually occurs at high energy ( > 1 MeV). (iii) Flaking: This formation takes place when almost the total area of the implanted spot leaves the surface with practically uniform thickness. Flaking can be induced at all energies under special implantation conditions, i.e., elevated target temperature and prolonged irradiation after blister rupture. Figure 22 shows some typical electron micrographs of these three types of surface deformation. Das and Kaminsky (1976) and Scherzer (1983) have listed the parameters affecting the gas-ion-induced surface modifications in detail and have reviewed extensively the experimental observations supporting the influencing factors. Following is a brief survey of the influence of some of the most important parameters on blistering. It must be stated at the outset that solubility and diffusivity of the implanted gas in metals are two of the important parameters affecting the blistering process. In general, hydrogen isotopes have higher solubility and diffusivity in most metals than inert gases such as helium, which is reflected in the fact that the dose rate and critical dose for blistering under hydrogen irradiation are considerably higher than that for helium. Moreover, in certain metals, e.g., Ti, Zr, Nb, and Ta, hydrogen reacts exothermically and forms a strong chemical bond with the surface (Scherzer, 1983). For these reasons, most of the work on blistering is concerned with He ions. The projectile energy determines the depth of implantation and hence the blister skin thickness, or “deckeldicke”, t , and the blister diameter D.One wellknown effect is that the ratio of blister lid thickness to projected helium range falls with energy from 3 for E < 5 keV towards unity above 100 keV (Roth, 1976; Risch et al., 1977). The fact that t , is 2-3 times larger than R , at low energies is a controversial point on the blistering models. The “deckeldicke” t , is often measured directly in units of distance by SEM or in units of target atoms/unit area by RBS. The direct measurements are affected to some extent by swelling of blister skin as discussed by St.-Jacques et al. (1978).This partly accounts for the thicker “deckeldicke” observed at low energies where relative swelling is expected to be larger. Emmoth (1983) compared the thicknesses of flakes measured by SEM and RBS for A1 and stainless steel in the energy range 20-80 keV. The SEM-measured values are always largest over the whole energy range, while the RBS measured values correspond very well with the projected range. This is in agreement with the earlier observations of Whitton et al. (1981), who noted a 30% greater thickness of Inconel-625 flakes measured by SEM when compared to that measured by RBS. It is further noted (Emmoth, 1983) that the relative swelling for flakes increases with

-

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FIG.22. Scanningelectron micrographs showing examples of (a) blister formation on an N b single crystal bombarded in random direction by 15 keV He+ ions [after Roth et a/., 19751; (b) exfoliation on Inconel type INCO-625 after 1 MeV He' bombardment [after Paszti et al., 1983al; and (c) flaking on Inconel type EP-753 after 1 MeV He' implantation [after Paszti et a/.. 1983al.

decreasing energy, being 10-20% at higher energies and 50-60X at lower energies. Quite recently, Whitton et al. (1988) pointed out that the skin thickness at the perimeter of the blister may be different from that near the center because of the change of angle of ion incidence to the blister surface during the growth phase. The diameter of the blister is roughly proportional to the energy of the projectile, and above a certain energy ( E > 1 MeV), only

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one large blister occupies almost the whole bombarded area (Das and Kaminsky, 1974). It is further proportional to t: with 0.85 Irn I1.5 (Scherzer, 1983). Temperature is one of the most important factors influencing the surface deformation. There appear to be four temperature ranges in which quite different blistering behaviour occurs (McCracken, 1975).At low temperatures (up to 300-400 K) regular hemispherical blisters occur; some of the blisters have caps that are lifted at the edges or lost completely. At intermediate temperatures (700-900 K) the surface flakes in a very irregular form. At high temperatures (- 1100 K) the surface again produces hemispherical blisters that tend to be larger than at low temperature. At very high temperatures (1500-1600 K), the surface is typified by a pinhole or spongelike configuration that should not be considered as blisters at all. No detailed mechanisms have been suggested to describe these features. They are possibly related to differences in the bubble growth mechanisms at different temperatures, and partly to changes in plasticity and yield strengths of the materials concerned. The critical dose determines the concentration of the implanted gas atoms needed for blistering. The maximum concentration is, however, limited by particle reflection and surface regression due to sputtering. The critical dose is found to increase slowly with the projectile energy (Das and Kaminsky, 1976; Saidoh et al., 1981).It is also observed that the dose for onset of the implanted gas reemission during bombardment approximately coincides with the critical dose for blister appearance (Erents and McCracken, 1973).Bauer (1978) summarized the critical dose behaviour of seven metals that were He-implanted at energies from 20 to 300 keV. The critical helium lattice concentration Cg, (expressed as He/metal ratio) for blistering is a strong function of the homologous temperature T/T, (T, is the melting temperature) and is given by (Wilson, 1984) C$, = 0.5 - (T/T,),

(54) for T/T, I0.4. Armstrong et al. (1981) studied the dependence of the critical dose for 200 keV D + blistering in Cu on target temperature. They observed three well-defined temperature regions between 120 and 380 K such that each region is characterized by a particular value of the critical dose that is independent of temperature. Blister morphology also changes abruptly in going from one temperature region to another. The flux of incident ions determines the rate of gas buildup near the implant depth, which is, however, affected by the rate of diffusion of the implanted gas to the bulk and to the surface. Because of the extremely low solubility and comparatively lower diffusivity of He in metals, helium blistering is relatively insensitive to incident flux. Conversely, because of the

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high diffusivity and solubility of hydrogen in metals, the likelihood of blistering is determined by a competition between the accumulation of hydrogen and its loss from the implant depth by diffusion. Therefore, the critical dose for hydrogen blistering depends on the flux density (Verbeek and Eckstein, 1974; Behrisch et al., 1976a; Moller et al., 1976). Another effect of high flux density is the formation of a local thermal spike in the bombarded spot, which in turn may change the blister morphology. The morphology of blisters formed in monocrystalline targets depends on the channeling of projectiles. Kaminsky and Das (1972, 1973a) investigated blistering of Nb monocrystals irradiated at 1173 K with 0.5 MeV He' ions. The results indicate a strong dependence of the blister shape and the orientation of the blisters with respect to each other on the crystallographic orientation of the target. The blister shape on the (1 11) surface plane reveals a threefold symmetry, and the prongs are aligned perfectly along the traces of (1 10) planes of the lattice. The blister density is lower by approximately two orders of magnitude for the channeled helium projectiles as compared to unchanneled ones. The average blister size is larger for axially channeled ions than for unchanneled ions. Similar observations were also made by Verbeek and Eckstein (1974), Roth et al. (1974), and Risch (1978). No detailed explanation for this directional effect has yet been put forward. In the following section, the formation and growth of bubbles are discussed, which is important for understanding the mechanism of blister formation. 3. Bubble Formation and Growth Bubbles are formed in solids by introducing insoluble gases to a high concentration of approximately one gas atom per bulk atom. Helium bubbles are observed in a large number of metals, and it is now an established fact that the bubbles are the precursor of blistering and flaking. It is known that helium is highly mobile as long as it occupies interstitial positions; the activation energy for interstitial migration of He in f.c.c. metals range from 0.1 to 0.4 eV (Reed, 1977; Melius et al., 1978).But it becomes deeply trapped in vacancies or at other lattice defects such as dislocations, grain boundaries, impurities, or precipitates because of the high binding energies; e.g., the binding energy of an He atom to a vacancy is 2.6 eV in Ni (Wilson et al., 1981).Small helium bubbles are thought to nucleate from the agglomeration of approximately six helium atoms in one lattice vacancy. These helium-vacancy clusters then grow by trap mutation. The term bubble is used for a gas-vacancy complex containing more vacancies than helium atoms. Surface modifications due to bubbles are easily understandable from the estimation of pressure of the implanted gas inside the bubble. If it is assumed

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that a bubble of radius R,, which contains gas at a pressure P, is in equilibrium under expansion because of the pressure and the surface energy increase, the relation between a bubble’s pressure and its radius is written as

where y is the bubble surface energy per unit area. For Ni, y = 2000 erg/cm2 (Trinkaus, 1982) yields an equilibrium gas pressure of 35 kbar for a typical radius R, = 12 8. This pressure is an order of magnitude higher than that obtained in laboratory experiments carried out to measure the equation of state (EOS) of gaseous helium. Empirical equations of state, such as the van der Waals’ law, which have been fitted to experimental data, cannot be extrapolated with confidence to “gas pressures”, which are close to solid-state pressures. A satisfactory empirical EOS based on experimental measurements has been developed by Mills et al. (1980)in the pressure range 2-20 kbar and temperature range 75-300 K. They express the molar volume V in cm3 within an accuracy of f0.3% in the above-specified range as V = (22.575

+ (-

+ 0.0064655T - 7.2645T-’/2)P-’/3

12.483 - 0.024549T)P-2’3

+ (1.0596 + 0.10604T - 19.641T-’” + 189.84T-’)P-’,

(56)

where P is the pressure in kbar and T is the absolute temperature. Attempts have also been made to derive an analytical expression for EOS for helium and other inert gases at high pressures. A nonattractive hard-sphere approximation represented by virial expansion in terms of reduced parameters z and w is a possible approach to a theoretical description of imperfect fluids. Ree and Hoover (1964) gave the first few accurately known virial coefficients in the form

z= 1

+ 4~ + lowz + 1 8 . 3 6 ~+~2 8 . 2 +~ ~3 9 . 5 +~ ~56.5w6**.,(57)

where z = PV/NkT is called compressibility and w = m3N/6V is called the packing fraction; s is the hard-sphere diameter. A few closed-form expressions of Eq. (57) have been used to find the EOS agreeing with the results of molecular dynamic simulation experiments on an ensemble of hard spheres. The assumption of a gas atom as a hard sphere at a high pressure leads to inaccurate results. The more realistic approach is to derive the hard-sphere diameter varying with density from a realistic potential and to use it in one of the closed-form expressions of Eq. (57). Accordingly, Wolfer (1981) used Beck’s interatomic potential of helium (Beck, 1968) to derive a theoretical EOS starting from the hard-sphere approximation of Carnahan and Starling

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131

(1969) with s varying with temperature and pressure. Trinkaus (1983) has calculated an EOS based on the adjustment of both the virial coefficients to agree at low densities and the empirical compressibility on freezing. For gaseous or fluid He, the final form is

where P=

VIP,

V, = 56T-”4exp(-0.145T+1’4)

in units of

A3,

z1 = 0.1225V1T0*555,

B = 170T-”3 - 1750/T z;V,

2:

in units of

A3,

-50.

For room temperature liquid He, Eq. (56) from Mills et a/. (1980) agrees with the calculations of Trinkaus [Eq. (58)l to within a few percent. Furthermore, Eq. (56), when used at a pressure 50 times higher than the range of its experimental validity, gives pressures for a given V differing from the theoretical values by no more than 50% even for solid helium. At present the EOS given by Eqs. (56) and (58) give the most acceptable values with a reasonable fit to the theory and experiment. Generally, it is difficult to determine the pressure of the bubbles directly; rather, one measures the density of the gas within the bubble and then uses the EOS for density-to-pressure conversion. The helium density NH, in a spherical bubble with radius R, is given by (Van Swijgenhoven et a/., 1983a)

where 0 is the implanted dose, f is the fraction of the implanted dose precipitated into the visible bubbles, A R p is the range straggling, and C , is the bubble density. Donnelly (1985) has reviewed the density and pressure of helium in bubbles, including a comprehensive discussion on the EOS formulated by different authors. At high temperatures where enough thermal vacancies are available, there will be a continual arrival of vacancies tending to make the bubble grow, and at the same time an equal rate of departure tending to make it shrink. The bubbles are thus in thermal equilibrium, and the gas pressure inside the bubble is given by Eq. (55). While at low temperatures

132

D. GHOSE AND S. B. KARMOHAPATRO

because of the absence of sufficient vacancy mobility, the bubbles are found to be overpressurized so that P > 2y/R,, and instead of a further increase in the volume of the bubble to an extent satisfying Eq. ( 5 5 ) , the free energy is stored as a pure shear strain around the bubble. Gas pressures in the range of tens to hundreds of kbar in the helium bubbles pressurized above the equilibrium level almost surely exist in some metals at least. Formation of solid Ar, Kr and Xe bubbles in various f.c.c. metals (vomFelde et al., 1984;Templier et al., 1984; Evans and Mazey, 1985) provides clear indication of the remarkably high pressures generated during bubble-growth processes by these gases also. An upper limit of pressure in an overpressurized helium bubble in Ni implanted with multienergy He ions ( E I 5.2 MeV) is measured by Haubold and Lin (1982) from a small-angle X-ray scattering study. They obtained a value of 300 kbar, which corresponds to a He density in the bubble of 2 helium per vacancy (He/V) using the EOS of Mills et al. (1980). Donnelly (1985) has compiled the values of maximum helium densities in bubbles in several metals determined from various experimental investigations with various ion doses. These values range between 0.3 and 5 He/V, which corresponds to 2.5 x 4.5 x loz3He-atom/cm3, some of which are derived on the assumption that all the implanted gas is concentrated in the observable bubbles. The question as to whether all the helium atoms reside in the observable bubbles, or a major fraction resides in small submicroscopic clusters distributed between the bubbles, is important for understanding the surface-modification and gasrelease processes. There are contradictory conclusions from experimental results; for example, for He in Al, Jager et al. (1982)found evidence that above 6 at % He concentration, most of the He is trapped in observable bubbles, whereas Johnson and Mazey (1980a,b) in an experiment involving He in Cu concluded that most of the gas is trapped outside the visible bubbles. The nonmonotonic variation of He density with ion dose at both low- and highenergy implants observed by Fenske (1979) reveals an enormously high pressure ( 6 Mbar) corresponding to the highest density (- 5 He/V) which is incompatible with the mechanical properties of metals. The conclusion is therefore drawn that a large percentage of the implanted helium, depending on the dose, is trapped in the submicroscopic defects. The recent study, by Van Swijgenhoven et al., of the bubble growth in Ni during 5 keV He' implantation (1983a,b; Van Swygenhoven and Stals, 1983) indicates that about 35% k 25% of the implanted helium precipitates into visible bubbles at the dose of 1017 ions/cm2, while the percentage increases to about 55% f 28% at the critical dose for blistering (5 x lOI7 ions/cm2). During He ion irradiation of Mo, Sass and Eyre (1973)first observed not only that high concentrations of nearly equally sized bubbles ( R , = 10 A) are developed, but also that the bubbles are mostly ordered on a space lattice in

-

-

SOLID SURFACES MODIFIED BY FAST ION BOMBARDMENT 0 0 0 0 0 . 0

0

0 0 0 .

0

0 0 0 0

0

0 0

0 0 0 . 0 0 0 0 0 0

0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 .

0 . 0 0 .

133

0 0

FIG.23. Illustration of bubble growth by loop punching. (a) Excess bubble pressure deforms surrounding atom planes. (b) Shunting process allows expansion of bubble and creation of interstitial loop. [After Evans, 1978.1

the host metal. Subsequent studies (Mazey et al., 1977; Johnson and Mazey, 1980a,b; Jager and Roth, 1980; Johnson et al., 1983) have shown that in the case of metals having a high degree of crystalline perfection within grains, the bubble superlattice was formed in all metals representing the three main crystal structures b.c.c., f.c.c., and h.c.p. at temperatures <0.3Tm. The mechanism of bubble growth depends on the number of external vacancies, either created thermally or by radiation damage during implantation. At low temperatures ( T < O.3Tm)where only insufficient radiation induced vacancies are available, a loop punching mechanism (Greenwood et al., 1959) has been proposed that would allow the bubbles to grow without the help of external vacancies by the emission of a cluster of interstitials (or dislocation loop), as sketched in Fig. 23. An alternative process of creating vacancies is the emission of self-interstitial atoms (SIA). This latter process requires a pressure an order of magnitude greater than that for the loop punching process and is therefore less favourable for bubble growth, but it is suggested to be operational only in the bubble nucleation phase. The punching of prismatic dislocation loops (i.e., burger vector normal to the plane of the loop) as a mechanism for stress relief was originally discussed by Seitz (1950). Lally and Partridge (1966) reported the first observation of such loops associated with gas bubbles in Mg quenched from high temperature in an atmosphere of Ar contaminated with air and moisture. They concluded that the observed loops had been punched out by hydrogen bubbles formed during the quench as a result of the decreasing solubility of hydrogen with temperature, which was subsequently confirmed by Wampler et al. (1976). Recently Evans et al. (1981, 1983) observed punching of loops from helium platelets and showed that such a mechanism can also be initiated by electron-beam effects during observation in TEM. For loop punching to be energetically possible, the free energy of a circular prismatic dislocation loop can be equated, following Greenwood et al. (1959), with the work done in expanding the bubble volume by AV. This yields the

134

D. CHOSE AND S. B. KARMOHAPATRO

minimum pressure, PLp,at which loop punching can occur: 2Y PLP RB

--+

Pb ln-,RDL 2xR,(1 - V) ro

where p is the shear modulus, v the Poisson ratio, b the burger vector of the emitted dislocation loop, ro ( 1:b) the core radius of the dislocation, and RDL ( N RB) the radius of the dislocation loop. There are variations in Eq. (60) found in the literature. For small bubbles of radii R, in the range 2b < R, < lob, Eq. (60) is replaced by 2Y PLP= Rn

Pb +Rn

‘v

2Y (5 to lo)-. R,

In a theoretical treatment, Trinkaus (1983), however, has concluded that Eq. (61) may only be correct to within a factor of two. The mechanism of loop formation is still not well understood. It is not clear why for small-size bubbles the expelled interstitials form threedimensional clusters near the bubble, whereas the self-interstitial atoms exceeding a number 13 form two-dimensional platelets (Ingle et al., 1981). In the derivation of Eq. (60), the elastic interactions between successively punched dislocations are ignored; such interactions have the effect of increasing the maximum pressure. Besides that, the assumption of an undamaged lattice is not a reasonable approximation since the lattice may also have small He clusters along with the visible bubbles. The bubbles cannot grow to an unlimited size. A mechanism for material failure in the surrounding of overpressurized bubbles was put forward by Auciello (1976), and the associated pressure was evaluated by Evans (1977, 1978). Over this critical pressure, interbubble fracture occurs, triggering the blister formation. Evans (1977, 1978) considers a set of identical coplanar overpressurized bubbles at some depth below the surface of a semi-infinite medium. The tensile stresses at the bubble surface will combine to give a resulting tensile stress in a direction perpendicular to the plane containing the bubbles and therefore tending to part the material at this plane. The pressure at which such a process occurs is obviously dependent on bubble density C , and the fracture strength of the material oF.The pressure PF for fracture between the bubbles is given by

A comparison of Eqs. (61) and (62)as a function of bubble radius shows that below a certain critical radius R;, PLpis always less than PF.That means for R, < R ; the bubble will relieve its excess internal pressure by loop punching

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135

until the two equations converge at R ; . At or above R ; , the interbubble fracture will occur. 4. Models of Blister Formation Two sets of condition have to be fulfilled for the appearance of blistering. (i) A peak of helium concentration must set up beneath the target surface. (ii) The He concentration at the peak must reach at least about 0.3 Helmetal. The first condition usually demands a monoenergetic ion with perpendicular angle of incidence, while the second condition defines the helium dose at which blister formation is initiated. Qualitative models for the formation of blisters have been suggested by a number of authors. These fall into two major categories. One is the gas pressure model, in which the buildup of excess gas pressure in the implant region of maximum gas concentration is the main driving force for the surface deformation leading to blister appearance. The other is the integrated lateral stress model, in which it is suggested that the large lateral stress introduced in the implanted layer leads to elastic instability and buckling of the implanted surface layer above the weakened interface region, and thus gas pressure is not the driving force behind the surface deformation. The experimental evidences on which the gas pressure model are based are (i) the observation of gas bursts and their correlation with the number of pits observed on the surface (Kaminsky, 1964; Thomas and Bauer, 1973);(ii) high symmetry of the blisters and the occurrence of blisters on both front and rear faces of a thin wedge-shaped Mo sample bombarded with He ions (Evans and Eyre, 1977); (iii) formation of extremely large blisters due to the lateral coalescence of small blisters with high density (Das and Kaminsky, 1973; Paszti et al., 1981; Saidoh et al., 1981); and (iv) the fact that at E > 100 keV, blister lid thickness (“deckeldicke”) is approximately the same as the mean range of the implanted ion (Kaminsky and Das, 1973b). Blistering was initially attributed to a sudden coalescence of small bubbles, which occurs when the density increases sufficiently to allow bubbles to touch (McCracken, 1975).This happens, of course, at a depth corresponding to the mean range of the incident ions. The coalescence of two bubbles at constant volume results in an excess internal pressure in the large bubble, because of the fall in the term 2y/R,. The situation is a runaway one until the pressure is relieved at the surface, by which time a blister is formed. Assuming the blister as a thin spherical shell clamped at its periphery with an internal pressure P, the blister diameter D is given by D = 4a,tB/P,

(63)

136

D. GHOSE AND S. B. KARMOHAPATRO

where tB is the blister lid thickness equal to R , , the projected range of the ion, and c,, is the yield strength of the material. Equation (63) predicts a linear relationship between blister diameter and lid thickness. The principal argument against the above model is that the lid thickness is appreciably larger than the depth of the helium peak, especially for E < 100 keV. To resolve the thick deckeldicke controversy, Evans (1977, 1978) developed a model in which blistering is initiated by the interbubble fracture of highly overpressurized helium bubbles. As discussed earlier, in the initial phase, the bubble grows by athermal processes such as loop punching, but with increasing bubble size the growth is governed by an interbubble fracture mechanism. At some critical depth from the irradiated surface, a layer of bubbles may have internal pressure equal to that required for interbubble fracture, PF.This creates an internal crack. If the pressure difference between the gas in the crack and gas in the bubble adjacent to the crack is sufficient, a process of “unzipping” layers of bubbles can take place, being able to start deforming the layer of material above the crack to give the final blister crosssection. The sequence of events is schematically outlined in Fig. 24. One important result of this model concerns the position of fracture plane; because of the usual displacement of damage and helium peaks relative to depth, this plane can lie well beyond the peak of the deposited helium distribution. This

BUBBLE P E S S U R L

(C

1

td)

w)

FIG.24. Interbubble fracture mechanism: (a) high density of overpressurized bubbles, (b) crack formation, (c) bubbles adjacent to original crack become involved to widen crack and increase pressure, (d) penny-shaped crack that either extends to cause flaking or (e) forms blister. [After Evans, 1978.1

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removes the difficulty, inherent in previous gas models, of reconciling measurements of blister lid thickness with the helium range. In passing it should be noted that the idea of interbubble fracture was first proposed by Auciello (1976). Here the fracture does not run parallel to the surface as in the Evans’ model (1977, 1978). However, Auciello’s model (1976) appears to be the only one that can explain rupture of blisters around the periphery and on the top of the cover as observed by Erents and McCracken (1973). Though the lateral stress model was originally developed to explain the low energy discrepancy between blister lid thickness and helium range (Behrisch et al., 1975a), the proponents of this model have criticized the gas pressure model also on the basis that (i) it cannot explain the relationship Dmpa t i / 2 between the most probable blister diameter Dmpand blister skin thickness t , (Roth, 1976), and (ii) only a small fraction of the total implanted helium is actually emitted during blistering (Behrisch et al., 1975b). The formation of lateral stress observed during bombardment is associated with the local helium-bubble swelling. For small bubble radii ( 510 A), the volume swelling is independent of bubble size and depends only on the helium lattice concentration. At bubble radii larger than about 30 A, the volume swelling for a given lattice concentration of helium atoms increases with the bubble size (Roth, 1976). Because of the proximity of the metal surface, the swelling can expand in the direction of the surface normal, while parallel to the surface no swelling is possible because of the contact to the nonimplanted material. EerNisse and Picraux (1977) measured the lateral stress integrated over the thickness of the implanted layer, oi, in He+bombarded Mo, Nb, and Al as a function of the implanted dose @, which shows a linear variation at low doses followed by a sublinear stage before falling relatively sharply in the region where surface blistering is initiated. The low-fluence results provide values for the induced volume expansion per implanted He atom. At high fluences, the integrated stress saturates and relieves. The saturation value, oi,max,is proportional to the yield stress o, of the material and is independent of the helium projected range. Considering the elastic instabilities of a circular plate subjected to lateral forces in the plane of the plate, it can be shown (EerNisse and Picraux, 1977) that the critical lateral force per unit length, oi,cr,at which buckling occurs is given by

where YM is the Young’s modulus, v is the Poisson ratio, tB and D are the thickness and diameter of the plate, respectively, and K is a geometric factor that ranges from 1.4 to 4.9 for elastic edge conditions ranging from a simply supported edge to a clamped edge, respectively. In the case of He-implanted and also that the shear failure takes place at layers, assuming that oi,cr = oi,max

138

D. CHOSE AND S. B. KARMOHAPATRO

the interface between the implanted layer and the bulk, it follows from Eq. (64) that D cc ti’’. Contrary to the gas pressure model, which necessitates “overpressurized” helium bubbles, this model does not require an explicit description of the microscopic behaviour of He in metals, though the origin of the stresses is the He in the lattice. The relation between the blister diameter and cover thickness, i.e., Dmpcc ti5,is considered as important evidence for the stress model. Das et al. (1978) measured the relation experimentally in Be, V, Ni, and Nb with great care for the diversity of the blister diameter in a given sample, which seems to have been neglected in the earlier data compilations. The results showed that the exponent of t B is strongly dependent on the type of the material (e.g., value of exponent varies from 0.85 for V to 1.25 for Be) and also on the target temperature; this does not support the lateral stress model. With this in view, Kamada and Higashida (1979) developed an interbubble fracture model of blistering that criticizes the objections raised against the gas pressure model. This model is based on the stress fields around a large lenticular bubble of diameter 2RLB parallel to a free surface at a depth h g . The bubble is loaded with a gas of pressure P. The components of the stress field are found to have square root singularities at the bubble tip. This means in real materials, plastic deformation must take place in such a region, which is called the plastic zone. This plastic zone must spread as the radius of the bubble increases. Since the lenticular bubble is similar to the tensile crack whose surfaces are subject to internal gas pressure, the plastic zone at the bubble tip extends farthest in the direction normal to the bubble surface. When the boundary of the plastic zone touches the free surface, the subsurface layer over the bubble may suffer general yielding and deform into a dome-shaped blister. It is shown that the blistering process can be separated into two factors: One is determined only by the geometry of the lenticular bubble, namely, by (hB/RLB),and the other is determined by physical properties of the materials and expressed as ( P / c , ) ~ . This latter factor, which is dependent on both the ion energy and the target materials, is responsible for the nonlinear dependence of the blister diameter on the cover thickness. Though this model clears some of the objections against the gas pressure model, the mechanism of the growth of the lenticular gas bubble is not satisfactorily understood. It cannot be formed by a simple crack extension mechanism in ductile materials, as the estimated internal gas pressure is far lower than the pressure necessary to satisfy the Griffith’s condition. In conclusion, controversy still exists regarding the two mechanisms to explain blistering. No model as yet can describe blister shape, size, and cover thickness in a quantitative way. Exact experimental data are also lacking to compare the models. While effects of lateral stress are identified as playing a major role in flaking, effects of gas pressure seem to be a dominant influence in

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139

blistering at lower temperature. However, it is now certain that both the stress and gas pressure are involved in evaluating the physical mechanism of surface deformation (Wolfer, 1980). 5. Flaking and Exfoliation Risch (1978) investigated blistering and flaking in Nb bombarded with 100 keV Hef ions. The current density at the critical dose of blistering seems to determine whether small discrete blisters are formed or flaking over a large area occurs. A high current density (-400 pA/cm2) shortly before reaching the critical dose results in flaking, whereas a low current density ( - 20 pA/cm2) results in small discrete blisters. Emmoth (1983) noted that for 75 keV Hef bombardment of 304 stainless steel, blisters are formed at room temperature, but at elevated temperature, above 373 K, the surface flakes. During 40 keV He+ irradiation of polycrystalline Al at 325 K, Braun and Emmoth (1976) observed a rapid -250-fold enhancement of optical photon intensity from sputtered excited Al atoms at a critical dose of 4 x 10'' Hef/cm2. It was shown that this effect is associated with a sudden increase in the erosion rate of the target due to flaking and also due to a rapid oxidation of the newly exposed surfaces. At very high dose and controlled target temperature (in the range 0.2Tm-0.4T,), multiple flaking may occur. While Kaminsky and Das (1978) demonstrated 15 successive generations of flaking from 316 stainless steel bombarded at 723 K with 100 keV He' to a total dose of 1.25 x lo2' ions/cm2, Whitton et al. (1981) observed as many as 39 repetitions in Inconel 625 with a dose of 3 x 10'' 100 keV Hef ions/cm2. The latter authors also observed a strong dose-rate dependence of the maximum number of flakes generated; decreasing the beam current from 640 pA/cm2 to 64 pA/cm2 results in a factor of 20 fewer flakes being generated for the same total dose. During repeated flaking, the crater area that is left decreases rapidly. When the crater diameter reduces to a minimum, the flaking eventually comes to an end (Emmoth, 1983). A comparative study of blistering and flaking induced in the same bombarded spot in the case of 200 keV D + bombardment of Cu (Johnson and Jones, 1984) reveals that the fracture plane of flakes is situated at somewhat shallower depth than that of blisters. Terreault (1980) studied the question of repetitive flaking in detail and predicted various blistering regimes by the ratio of the range profile width (FWHM) to the mean projected range R,. According to him, blistering or flaking will be repetitive as long as FWHMIR, < 0.7. The works of Martel et al. (19741, Behrisch et al. (1976b) and Gusev et al. (1979), however, show that at high enough doses, blisters disappear and a sponge-like equilibrium surface structure is developed. These observations led them to the conclusion that the blistering process is transient and not continuous.

140

D. GHOSE AND S. B. KARMOHAPATRO

Studies of surface deformations caused by MeV energy helium implantation in which mainly exfoliation and flaking dominated are relatively scarce. The Hungarian group (Mezey et al., 1987)have done some work in this direction. The transition energy at which the blistering process turns into exfoliation is found to be material-dependent. While gold exhibits helium exfoliation at 2 MeV (Mezey et al., 1982), for Inconel and stainless steel the transition energy at room temperature is below 1 MeV (Paszti et al., 1983a). On the basis of the results of 3.25 MeV helium exfoliation in a gold target, Paszti et al. (1981) concluded that the relationship between blister skin thickness and diameter experienced at lower bombarding energies seems to be invalid at high bombarding energies. The only limiting factor in the diameter is the size of the implanted spot. They also gave a speculative model for highenergy blister formation. Bhattacharya et al. (1988) bombarded a 100-pmthick W sheet with 2.6 x lo'* 28.7 MeV 01 particles/cm2 from the Calcutta variable-energy cyclotron. The projected range of the ion is comparable to the thickness of the specimen. A large elongated exfoliation (length 1500 pm and breadth 1000 pm) with rupture at some portion of the cover was observed only on the reverse unbombarded surface (Fig. 25). This observation lends support to the gas pressure model of blister formation. Metallic glasses, however, show different behaviour with MeV helium implantation (Manuaba et al., 1982; Paszti et al., 1983b,c).The surfaces flake immediately the critical dose is reached. Blistering occurs only when the bombardment is done at elevated temperature. On the surface left behind the flaked layer, a peculiar wave pattern formation can be observed. A similar pattern accompanied by

-

-

FIG.25. Scanning electron micrograph showing exfoliation on the rear unbombarded face of a W sample after 28.7 MeV ct bombardment. The viewing angle in the microscope is 70". White markers = 100 pm.[After Bhattacharya et al.,1988.1

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FIG.26. Wave structure on Metglass 2826A after flaking induced by 2 MeV He+ bombardment. White scale marker is 20 pn. [After Manuaba el al., 1982.1

flaking was also observed in a helium-implanted silicon surface (Paszti et al., 1985). The waves consisted of elevations of asymmetric triangular crosssection and were formed only at temperatures below the crystallization temperature. Figure 26 shows an example of very regular pattern formation on Metglass 2826A after flaking. This can be compared with the ripple structure observed in Si surface eroded by very high-dose heavy-ion sputtering (Carter et al., 1977). The periodicity of the wave structure can extend to several mm in length. The wavelength varies between 0.9 and 1.8 pm. In some cases the pattern is characterized by diffraction, interference and island-like formation. Hajdu et al. (1987; Hajdu, 1988) proposed a mechanical stress model to explain the phenomena. It is thought that the large lateral stresses developed by ion implantation, as discussed by EerNisse and Picraux (1977), are relaxed by forming wrinkles and corrugations if not relaxed otherwise, e.g., by forming blisters. An approximate analytical calculation gives the wavelength of wrinkling as (Hajdu, 1988) =

10.2 A R p ,

(65)

where A R p is the projected range straggling. This model, like the stress model of blistering, suggests the evolution of the wave pattern around the depth of maximum ion penetration, and unless it is near the surface, the pattern will be observable after removal of the uppermost layers. Such a topography once

142

D. CHOSE AND S. B. KARMOHAPATRO

formed is not lost even if a thickness greater than the projected range is removed. Finally, it should be noted that formation of voids can also result in topographical changes, which is discussed in the following section. 6. Surface Modification due to Void Swelling Cawthorne and Fulton (1967) discovered the void swelling phenomenon during examination of stainless steel fuel claddings exposed to high doses of fast neutrons in a reactor. The development of internal porosity in the form of small cavities (- 100 A) results in an overall volume increase, i.e., swelling of the irradiated materials from a few percent to an order of 10% in specific cases. In most of the materials voids generally form and grow in the temperature range of 0.3T, to O S T , . At very low temperatures (<0.3Tm),the mobility of vacancies is small so that recombination with interstitials is more prominent than migration to a sink to form a void. At very high temperatures ( > 0.5 T , ) , radiation-induced vacancies are fewer in number than thermal vacancies, prohibiting the supersaturation of vacancies that provides the driving force for void nucleation and growth. The sufficient conditions for void swelling to occur in the appropriate temperature range are the presence of biased sinks such as dislocations for interstitials and of neutral sinks such as gas bubbles. The growth rate of voids depends on the competition from all other sinks. Consequently, not every vacancy migrates to form a void. In fact, nearly one in one thousand of the vacancies produced accounts for the volume change, since significant swelling in excess of nearly 0.1% is observed at displacement doses of 1 to 10 displacements per atom (dpa) (Nelson, 1976). The use of ion beams to study void swelling was introduced by Nelson and Mazey (1969; Nelson et al., 1970) at Harwell. They showed prior implantation of helium is effective in aiding void nucleation. Many other workers followed the Harwell group with ions with H+ to Ta' in the energy range to lo-' 100 keV to -50 MeV and the atom displacement rates from (dpa) s-' (Johnston and Rosolowski, 1976). Intense electron beams of energies between 0.5 and 1 MeV from a high-voltage electron microscope (HVEM) are also used for void studies (Norris, l970,1971a, b), where in-situ production and observation of damage structure can be performed. Such experiments are initiated with a view to simulating the damages produced by fast neutrons in reactor materials. Marwick (1975) showed that nickel-ion-induced displacement damages are a close approximation to reactor damages, while Johnston et al. (1973, 1974) showed that void swellings produced by Ni-ion bombardments are similar in terms of void densities, void diameters, and total swellings to those in-reactor when compared at the same damage level and at the respective peak-swelling temperatures.

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Similar to ordering of gas bubbles, voids can form a regular array on the host lattice as observed first by Evans (1971a, b) in a high-purity Mo single crystal irradiated with 2 MeV nitrogen ions. The void superlattices have the same symmetry and alignment as the host lattices. The average void radius is typically a few tens of angstroms, and the lattice constant ranges from one to a few hundred angstroms, which is, however, much higher than for bubble lattices (Krishan, 1982). It has been suggested (Stoneham, 1975) that void ordering takes place mainly in four stages: (i) the initial formation of many small voids distributed at random; (ii) growth of large voids by coalescence of smaller voids; (iii) development of small local regions where voids start having spatially ordered correlations; and (iv) spreading of these ordered local regions to the adjacent ones. In the case of a bubble superlattice, similar stages are proposed, but in addition to these four stages a fifth stage has been observed in which some bubbles are interconnected forming pipe-like channels close to the surface (Johnson and Mazey, 1980b; Jager and Roth, 1980).Quite recently, Evans (1985,1987) proposed that void and bubble lattice formation in metals could be explained by the two-dimensional diffusion of self-interstitial atoms on close-packed planes. Since the stress model of gas blistering accounts some of the experimental results, one may expect analogous surface structures involving void swelling, where the stress systems should be similar. In cases of large void swelling (greater than 20%), Johnston and Rosolowski (1976) could show that the integrated swelling is totally reflected in the step height between bombarded and shielded regions. These authors also observed some interesting changes in surface topography in void-swelling studies, which are not related to sputtering phenomena because of the high energies and temperatures used. Different elevations of grain surfaces, gross unevenness at large swellings, development of facets on certain grain surfaces, and formation of ridges at grain boundaries are the characteristic features of Ni-ion-bombarded stainless steel surfaces. Very recently, Ghose er al. (1984b, 1987)reported blister-like structures on both sides of Ta foils during 30-40 MeV a-particle bombardment. The blisters are mainly three-pronged, mixed with a substantial number of one-pronged and two-pronged ones (Fig. 27), and have a close similarity with the gas blisters previously observed on Nb single crystals bombarded by 0.5 MeV Hef ions at 1173 K (Kaminsky and Das, 1972,1973a). Since the foil thickness was much less compared to the projected range of the ion, the observed features are not related to gas bubbles. These may be attributed to void swelling, which provides great compressive stress parallel to the surface. It is thought that in addition to the displacement damage, the formation of a beam-induced local thermal spike and the presence of oxygen accentuate the swelling phenomenon, the collective effect of which is manifested in the form of surface structures. In passing it should be mentioned that Wilson (1982,

144

D. GHOSE AND S . B. KARMOHAPATRO

FIG.27. (a) Electron micrograph of 40 MeV a-bombarded Ta foil showing pronged blisters. (b) is a higher magnification micrograph of the u-bombarded Ta foil containing two threepronged and one two-pronged blisters. The viewing angle in the microscope is 33.5". White markers = 1 pm. [After Ghose et a[.,1987.1

1989 also observed topographical changes due to voids in case of low-energy heavy-ion-implanted semiconductors. Holes first appear in the surface at relatively low doses. As the ion dose increases, the holes grow to form a cellular structure that coarsens until a dynamic equilibrium is established. It is proposed that the cellular structure is the result of void formation combined with sputter etching.

IV. SUMMARY

To summarize, this review presents some pertinent aspects of ion-induced surface modifications. The first part deals with surface structures developed by ion-beam sputtering. A frequently appearing phenomenon in sputtering

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experiments is the development of cones or pyramids. Though the involvement of impurities in the formation of conical protrusions is well documented, the exact mechanism for nucleation of cones is still not well understood. It is not clear whether “intrinsic” effects, which arise from interactions of the ionsolid system alone, and “extrinsic” effects, which arise from perturbations of the ion-solid interactions caused by the presence of impurities and convex-up asperities on the solid surface, act separately or in concert in the development of cones. The wide belief that the impurities should have lower sputtering yields than the matrix materials is not always correct, as recently pointed out by Wehner (1985), where it is shown that only in the cases where the seed materials have a higher melting point are the cones formed. However, it is established that whatever the mechanism of cone nucleation is, it is the angular dependence of the sputtering yield of the cone material that largely determines the final shape of the cone. The formalism of Carter et al. (1971, 1973; Nobes et al., 1969) most clearly explains the evolution of cones and can be applied to predict the critical doses for cone formation and disappearance. A more complete description of the evolution of cones, however, needs the introduction of secondary and tertiary effects, the redeposition of sputtered materials, and the effects of crystallinity. An important aspect is the question of stability of cones under prolonged bombardment. It is known that isolated cones are generally not stable under ion bombardment. But under certain conditions, e.g., continual supply of seed atoms, or particular target crystallography, e.g., (1 1 3 1) (Whitton, 1986), the dense arrays of cones formed are found to be stable. This apparent stability is suggested to be due to continuous disappearance and regeneration of individual cones. Alternatively, if one considers the erosion by primary beam only, then for a dense array of cones there is no reference slope with respect to which the cones could recede (Auciello, 1982); consequently, the array would be stable. It is interesting to note that the semiconductors are not as susceptible to cone formation as the metals. This indicates that the structural state of the target influences the type of the topographical features. It has been demonstrated by Whitton and Grant (1981) that solids that cannot retain long-range order of the crystal structure under ion bombardment are very unlikely to develop conical features. The cone or faceted surface morphology has a strong influence in the angular distribution of sputtering yield as well as the total yield measurements. It also gives rise to poor depth resolution in some surface analytical techniques such as SIMS. The theory of Littmark and Hofer (1978) presents some qualitative information on these aspects. The second part of the present work concerns the surface modifications due to gas ion implantation, namely, blistering. Helium blistering is more easily observed than hydrogen blistering. Though the nucleation of helium gas bubbles is more or less understood, whether all implanted helium is accommodated in bubbles, or whether a considerable fraction of the implanted helium resides in clusters outside the bubble, is still a matter of debate. There

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are several proposals as to how bubbles gain vacancies by athermal processes that include SIA emission and dislocation loop punching, but exact details are not yet available. However, there is ample evidence that helium bubbles are pressurized far beyond the equilibrium level. The controversy between the gas-driven and stress-driven mechanisms of blistering is not resolved, but the final description seems to be a kind of in-between. Since the stress system in void swelling is similar to that of gas bubbles, there is no reason why analogous stress-induced relief structures should not also develop in this case. In fact, the work of Johnston and Rosolowski (1976) indicates that surface topography could also be developed for large void swelling. More investigations in this subject are needed. An important question is sometimes raised whether the blistering process is transient or continuous. It has been found that under certain circumstances blistering and flaking are repetitive, but the evidence is not conclusive. Recent experiments suggest that multiple energy multiangle ion bombardment and a rough surface can reduce blistering. These conditions prevail in a CTR machine; consequently, the blistering phenomena may not be a serious problem in fusion as was initially envisaged. Nevertheless, such experiments deserve attention on their own merit, since these will improve the understanding of the underlying mechanism of particle interaction with solids.

ACKNOWLEDGMENTS The authors thank Mr. M. C. Das for his untiring assistance in the preparation of several versions of the manuscript.

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ADVANCES IN ELECTRONICS AND ELtCTRON PHYSICS VOL 79

Scanning Tunneling Microscopy: A Mature Surface-Science Technique L. L . SOETHOUT H . VAN KEMPEN Research Institute f o r Materials. University gf Nijmegen Nijmegen. The Netherlands

G . F. A . VAN DE WALLE Philips Research Laboratory Eindhoven The Netherlands

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I . Introduction . . . . . . . . I1. Modes of Operation . . . . . . A . Microscopy . . . . . . . . B. Barrier-Height Profiling . . . C. Elastic Tunneling Spectroscopy. D . Inelastic Tunneling Spectroscopy 111.

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I. INTRODUCTION Scanning tunneling microscopy (STM) is a relatively young surfacescience technique. It exploits vacuum tunneling between a sharp tip and a second electrode. Upon application of a voltage between both electrodes, a current will flow that depends exponentially on the distance between the electrodes. This exponential dependence was measured for the first time in a metal-vacuum-metal tunnel junction by Young et al. (1971). They also realized that the structure of the surface of the second electrode could be imaged by scanning the tip along that surface under control of a feedback system to maintain a constant tunnel current. This resulted in the construction of a microscope, the so-called topografiner (Young et al., 1972), yielding a resolution of a few hundreds of angstroms. The topografiner could only be operated in the field-emission regime, i.e., at 100- to 1000-A gap distances, because of the lack of vibration isolation. It was not until 1982 that Rohrer, Binnig and co-workers succeeded in solving the vibrational problems. They were able to obtain stable and reproducible vacuum-tunneling characteristics at small gap spacings (Binnig et al., 1982a). The first topographic imaging in this regime gave a resolution of a few angstroms (Binnig et al., 1982b), much better than expected. Apparently the tunnel current is confined to an atomic-scale area by a combined effect of the exponential current-distance dependence and a very small protrusion at the apex of the tip. This opened the possibility of real-space imaging of atomic structures, as was demonstrated for the first time on Si(ll1) (7 x 7) (Binnig et al., 1983a). Mainly because of the atomic resolution, STM has become one of the fastest growing fields of surface science. The importance of the STM development was stressed by the award of the Nobel Prize in physics to Rohrer and Binnig in 1986. A rapidly growing number of institutes have become involved in this area, causing a still increasing stream of publications. Since 1983,the number of submitted publications roughly doubled each year, resultingin a total number of over 800 in 1988. Since 1986,yearly international conferences devoted to STM and related topics have been organized, which are visited by an increasing number of scientists. Also, commercially built STMs (we use the abbreviation STM both for the instrument and for the technique) can be purchased now from several companies. The aim of this review paper is to present the state of the art of the achievements of STM. The paper covers the STM literature published before 1989.The theoretical concept of STM is treated, together with its principle of operation and the various detection modes. The present status of instrumentation and applications is given, followed by a brief outline of “spinoff”applications related to STM.

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11. MODESOF OPERATION A. Microscopy

The scanning tunneling microscope is capable of three-dimensional imaging of surface structures on an atomic scale. Periodicity of the structures is not required. The sample has to be electrically conductive to some extent, since it forms one of the electrodes of a vacuum tunnel junction. The other electrode is shaped into a sharp tip and acts as the probe with which the surface properties of the sample are investigated. This tip is mounted on an electromechanical transducer consisting of piezoelectric ceramic elements. In this way the distance between the tip and the sample and the lateral position of the tip can be controlled. When a voltage is applied to the piezoelectric z-drive, the tip can be moved perpendicular to the sample surface, and in that way the distance between the electrodes is varied. The tip can be scanned along the sample surface by applying appropriate ramps to the piezoelectric x- and ydrives. A bias voltage, typically between - 2 and + 2 V, applied to the junction causes a tunnel current to flow, if the electrodes are close enough together. The fact that the tunnel current is very sensitive to variations in the barrier width between the tip and the sample forms the key element of the STM operation. Since the tip in the STM setup is sharp on an atomic scale, the strong exponential decay of the tunnel current will confine the current to flow in a small channel between the outermost part of the tip and the sample. The tunnel current therefore contains information on the local surface structure (see Fig. 1). Often an approximate equation is used to express the tunnel current I in terms of the barrier with s (Binnig et al., 1982a): I = VC(V )exp( - ~

K ~ s ) ,

(1)

where C ( V )describes deviations from Ohm’s law, and K~ = [(2m/h2)4I1/’is the inverse decay length for elctrons in vacuum. rn is the electron mass; 4 is the averaged barrier height, often replaced by the averaged work function of both In electrodes. The magnitude of (2m/h2)”’ is approximately 0.5 eV-li2 k’. an STM geometry a typical barrier has a width of a few angstroms, when the tunnel current is in the nA region. The STM can be operated in various modes. The two most common modes are described below: THE CONSTANT-CURRENT MODE. Through the use of a control unit, which regulates the voltage over the z-drive, a preset tunnel current can be established and maintained. Any change in current will be corrected by a feedback signal to the z-drive, which will position the tip at a constant-current level above the surface. When the tip is scanned along the surface, it will follow

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FIG. 1. Principle of STM operation. The tunnel junction consists of an atomically sharp tip opposite to the sample. The main part of the tunnel current flows from the apex of the tip, resulting in only a small tunnel channel. This explains the atomic lateral resolution. [After Binnig and Rohrer (1987).]

contours of constant current. Given a linear behavior of the transducers, the feedback signal V, at the coordinates (V’, V,)directly yields the topography of the surface. The tip scan rate is typically around 10 Hz and is limited by the response time of the feedback loop and the inertia of the tip motion. THE CURRENT-IMAGING MODE. The tip is scanned across the surface while the variations in the tunnel current are detected. In this case the feedback loop is absent or only keeps the average tunnel current constant. The current I at coordinates (V’, V,)indirectly yields information on the surface structure of the sample. This method can be applied only to very flat samples, since variations in height on the order of the barrier width will cause collisions between tip and sample. In this mode the scan rate can be much higher than in the case of the constant-current mode, i.e., typically 1 kHz. In both modes the applied tunnel voltage is assumed to be constant during the scan. Alternatively, the STM can also operate at a constant applied tunnel current. In this case the tunnel voltage is compared to a reference voltage, while the error signal is used for the feedback (Binnig et al., 1984a). According to Eq. (l),pure structural information is only obtained when the work function 4 and the prefactor C (V ) are constant over the scanned area. When these quantities are not constant, the interpretation of the images can be difficult. However, usually the changes in 4 are small and will hardly affect the profile. Section 1I.B will deal with the 4 dependence of the tunnel current and

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will give methods of separating variations in 4 from topographic variations. Variations in C(V ) as a function of lateral position are often more important. Strictly speaking, the STM images the electron distribution at the sample surface, which can deviate severely from the position of the surface atoms. C( V ) contains structural information on the electron surface states that determine the electron density. The voltage V determines the energy of the electron surface states that are involved in the tunnel process. This makes STM a spectroscopic tool as well. Details are given in Section 1I.C. An important criterion for a microscope is its resolution. In the case of STM, the variations in distance between sample and tip are detected via changes in the tunnel current. Because of the exponential dependence of the tunnel current on the distance and the high precision with which a current can be measured, the vertical resolution of the microscope easily could range below 0.01 A. A higher precision is usually not feasible because of the mechanical stability of the instrument. Laterally, structural features with details on an atomic scale ( < 5 A) are resolved, although the radius of the tip is typically a few hundred angstroms. Because of the exponential dependence of the tunnel current on the barrier width, the electrons will be confined to a narrow channel between the outermost atoms of the tip and of the surface. Those surface atoms that are one lattice spacing away will have a negligible contribution. The ideal situation would be a single atom at the apex of the tip. This configuration has been the starting point of several theoretical models for the evaluation of the lateral resolution (Tersoff and Hamann, 1983, 1985; Garcia et al., 1983; Stoll et al., 1984).In many cases a resolution of 2 A has been obtained experimentally, which indicates that the tip indeed consists of only one atom. To assure the monoatomic character of the tip, several methods for tip preparation have been developed (see Section 1II.C). Several experiments have shown the importance of tip effects in STM imaging. One such effect is that an increased tip size lowers the corrugation of STM images. This was demonstrated on Au(lll)(l x 2) and on Au( loo)(1 x 5) by Kuk and Silverman (1986) and Kuk et al. (1988). Another effect involves the shape of the tip, resulting in asymmetric STM images, as in images of the Si(111)(7 x 7) reconstruction by Berghaus et al. (1988a,b). Tunneling from more than one tip causes different parts of the sample surface to be imaged simultaneously. The total image is then a superposition of several single-tip images. Double-tip effects were observed by Park et al. (1987) on Si(l11), resulting in a superposition of two (7 x 7) images. These tip effects were found to change sometimes with bias, which indicates chemically different tips (Park et al., 1988a).On graphite, multiple-tip effects result in an apparent change of the shape of the unit cell (Mizes et al., 1987).The shape of the tip on a larger scale is important when rough surfaces are imaged. Surface

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structures comparable to or smaller than the dimensions of the tip (the radius of curvature is a good indication) are not represented correctly by the STM image, since the image will also contain information on the tip (see Abellan et al., 1987;Chicon et al., 1987).In the extreme case that the tip scans a whisker on the surface, the image will only contain information on the tip (i.e., the role of tip and sample is interchanged). B. Barrier-Height ProJiiing

Apart from imaging surface structures, which is basically done by controlling the width s of the potential barrier, STM can also provide information on the height 4 of the barrier. As already mentioned in Section II.A, constant-current profiles are in fact a mixture of structural, chemical and electronic properties of the surface. This is because the complete expression in Eq. (1) is kept constant, rather than s only. Corrugation detected on a perfectly flat surface would therefore correspond to changes in 4 provided that there are no other electronic effects (i.e., the factor C(V ) in Eq. (1) must be independent of x and y). In principle, one can determine the magnitude of 4 by measuring variations in barrier width s as a function of current I when the feedback system is working (Binnig et al., 1982a).Alternatively, one can measure I as a function of s by decoupling the feedback system for a short time. However, the most common method is by an ac modulation of the barrier width. With this method one can in principle separate the information on the barrier height from structural information. A small modulation (corresponding to a few tenths of an angstrom) of the voltage of the z-drive, with a frequency well above the cutoff frequency of the feedback system, will superpose an ac component onto the constant current. This signal can be detected with lock-in techniques. It follows from Eq. (1) that the ratio between the modulation in current and distance is given by

A typical modulation frequency is 2 kHz, limited by the mechanical stiffness of the tip scan unit. Faster modulation can be applied when a light source is used for the distance modulation, by means of a modulated heat dissipation in the sample (Amer et al., 1986). When the barrier width s is large (ie., > 5 A), the barrier height 4 becomes independent of s, making d l / d s oc 41i21. Then 4 can be identified with the average work function of both electrodes. At small values of s, however, 4 depends on the barrier width, because the image force drastically lowers the barrier.

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dr (nA/A) ds 0.8-

I

0

0.4

0.8

I (nA) FIG. 2. dl/ds as afunction of the average tunnel current for a tungsten tip and a silver sample. The barrier height, estimated from the slope to be I eV, is smaller than the expected average work function of 4.4 eV.

d l l d s plotted as a function of I should give an idea about the average work function of the metals involved, at least for small currents. The expected linear dependence is measured in most experiments, but the slope corresponding to &is generally smaller than expected from other work-function data (see Fig. 2). On clean, well-prepared surfaces a reduction of 50% is often observed. Binnig et al. (1984a) have calculated the influence of the image potential on the observed barrier height. A square barrier, reduced by the image potential, is approximated by a lowered square barrier with height

4(d) = 4 0 - aid3

(3)

where do is the original barrier height and d is the distance between the two image planes, i.e., d = s - b, b z 1.5 A. CI is a constant with value 9.97 eV A. Substituting this 4 into Eq. (2) gives, to first order in l/d, no influence on the slope of d l l d s versus s:

The only influence of the image potential on the tunnel current is an extra factor, independent of s:

I x I , exp[ -2(2rnlh2)”24,!j2(b- a/24,)],

(5)

where lois the tunnel current without the image potential. Their experiments on cleaned samples agree with these results.

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In Section 1I.A another method for STM was mentioned, in which the tunnel voltage is kept constant by a feedback system when a constant current is applied. Determination of the barrier height in this setup by measuring dV/ds, which should give the same result on theoretical grounds (except for its sign), yields drastically lower values in experiment (Binnig et a/., 1984a). This discrepancy can be reasonably explained by considering the effects on the barrier shape when the barrier width is varied at constant current and at constant voltage (Payne and Inkson, 1985). Also, the dependence on the topography has to be accounted for, because the detected current modulation underestimates 4 when the surface under the tip is not perpendicular to the direction of the modulation (Binnig and Rohrer, 1983). However, all these arguments cannot explain the very low barrier heights (one order of magnitude smaller than expected) that are sometimes observed. Therefore Coombs and Pethica (1986) proposed a model in which the actual barrier-width modulation is reduced by elastic forces between sample and tip. These forces are transferred by an oxide layer or by other adsorbates present in the barrier. The changes in 4 can also be monitored as a function of position; then, a barrier-height profile of the surface can be measured. Changes will occur on spots where the local charge distribution is different from its environment. This occurs, for instance, at a sharp edge or a grain boundary, at planes with a differentcrystallographic orientation, or at a site where an adsorbate is bound to the surface. Binnig and Rohrer (1983) have monitored Au islands on a Si substrate in this way (Fig. 3). On an atomic level, differences in barrier height

5 0 A PER DIV. FIG.3. (a) Topographic and (b) work function images of Au islands deposited on a silicon substrate. The effect of a change in work function is much stronger than the corresponding topographic change. [After Binnig and Rohrer (1983).]

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can also be observed (Kuk er al., 1987a),even in ambient air (Marchon et al., 1988a). In combination with known decoration techniques and Auger electron spectroscopy (AES), a local chemical fingerprint of the surface is feasible. An integrated STM/AES setup was built by Reihl and Gimzewski (1987). C . Elastic Tunneling Spectroscopy

As was already indicated in Section II.A, the voltage applied to the tunnel junction also is an important parameter. It determines which electron states of the sample and the tip contribute to the tunnel current. When the sample is biased positively with respect to the tip (i.e., V > 0 in Eq. (l)), the filled states of the tip between EF - eV and EF,and the empty states of the sample between E F and EF + eV, will be monitored (Baratoff, 1984;Tersoff and Hamann, 1983, 1985),as is shown in Fig. 4b. This implies that the bias can have a drastic effect on the topographic image when the density of states is a function of lateral position (see Figs. 4a and c). Another effect is that I - V characteristics are no longer linear in the case that the electrodes are not simple free-electron metals. In Eq. (1) this is represented by the factor C( V ) .The electrode properties that play a role in C( V )can be determined in the transfer Hamiltonian formalism of tunneling, as is sketched in Section 1V.C. This leads to the following formulation of the tunnel current at zero temperature: I ( V ) = (4ne/h)

jEF

d E I M ( E , V)I2p,(E)pS(r,E

+ ev)

(6)

EF-eV

(cf. Eq. (37) and Selloni et al., 1985,1988).p , ( E )represents the density of states (DOS) of the tip; ps(r,E + e V ) is the local density of states (LDOS) of the sample, evaluated at the position of the tip. M ( E , V ) is the tunnel matrix element, which often is assumed to be constant. In the case of a constant (L)DOSand a constant barrier width, I versus V will show an ohmic behavior. Changes in the LDOS will give a small additional structure on top of this. This additional structure is more pronounced when d l / d V is determined versus V. Filled and empty states with maximum energy (respectively, EF and E , + e V ) will contribute predominantly to the current because they see the smallest barrier width; i.e., M ( E , V ) is largest for such states. In order to detect possible LDOS variations several techniques are used. AC VOLTAGE MODULATION ON TOPOF A SLOWVOLTAGE SWEEP. When the modulation is above the feedback cutoff frequency, d l / d V can be detected by a lock-in amplifier (Becker et al., 1985a; Salvan et al., 1985; van de Walle et al., 1987a). Because the average tunnel current is kept constant during the slow voltage sweep, the barrier width is adjusted with increasing voltage, which

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SURFACE STATES

FIG.4. Principle of spectroscopy with STM. (a) The tip is situated above a surface with a buckling between the occupied (full figures) and empty (dashed figures) surface states. (b) Energy diagram of the tip-sample system. The density of states D, of the sample, associated with the occupied and empty states, is indicated. When the tip is positively biased (solid lines) with respect to the sample, tunneling takes places from the sample states with an energy between E , - el/ and E , . A negatively biased tip (dashed lines) results in tunneling to the empty sample states with an energy between E , and E , + eV. (c) The effect on the topographic image of tunneling at positive (solid line) and negative (dashed line) tip bias. [After Baratoff (1984).]

keeps the electric field limited. A drawback of this method is the fact that the spectral features are on top of a diverging conductance towards lower voltages. Plotting (d/dL')/(Z/V) does overcome this problem and gives a better representation of the LDOS (Stroscio et al., 1986). Experimentally the problem can be avoided by regulating the junction at a constant resistance value, which yields a nearly constant tip-sample separation during a voltage sweep (Elrod et al., 1984; Kaiser and Jaklevic, 1986). FASTVOLTAGE SWEEP. Reihl et al. (1986) sweep the voltage with a frequency well above the cutoff frequency of the feedback system. In this way a local I - V curve is obtained at constant barrier width.

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VOLTAGE SWEEP AT CLAMPED CONSTANT DISTANCE.Schroer and Becker (1986) developed a method, which they called current-imaging tunneling spectroscopy (CITS). Here the feedback system is disconnected during the voltage sweep, while the voltage on the z-drive is clamped, such that the distance s does not change. This technique is now commonly used (e.g., Hamers e l al., 1986a; Berghaus et af., 1988b; Bando et a!., 1988). All three spectroscopic modes have spatial resolution. In the latter two modes an I - V characteristic can be measured at each topographic point. In the first method the tunnel bias is set to a specific feature in the DOS at a certain energy eV, after which the spatial distribution of this feature can be obtained. In all cases the conventional topography is contained in the feedback signal. Especially on semiconductors with characteristic dangling bonds, this so-called scanning tunneling spectroscopy (STS) can render valuable information on the local electronic (re) arrangement of the top layers. The first experimental results were presented by Elrod et al. (1984). They performed tunneling spectroscopy on Nb at low temperatures and showed the presence of the superconducting gap in their spectra. For DOS fluctuations in normal metals, the signals will be less intense and less sharp. Both bulk and surface contributions are predicted to be present (Selloni et al., 1985),but they can in principle be separated because of their different attenuation in the barrier. Surface states and dangling-bond-like states will show up in the spectra as sharp features because of their long lifetime, especially when situated in a band gap of the bulk DOS projected onto the surface (Baratoff, 1984).At higher voltages other phenomena occur that are related to resonant states in the vacuum barrier. These states are identified as standing waves, arising from the reflection of electrons at the edges of the potential well between the slanting tunnel barrier and the surface of the positive electrode. These image states lead to sharp peaks in the spectra, the so-called Gundlach oscillations, for eV > 4, as seen by several groups (Binnig et al., 1985a; Becker et al., 1985a). Since the energy levels of these states strongly depend on the exact shape of the barrier and the electrode surface, they were hardly observed in conventional MIM junctions, as a result of averaging over all tunneling sites. Compared to other spectroscopic surface techniques, STS is sensitive to states in the outermost surface layers only, because of the dependence on wave-function overlap, whereas, for example, ultraviolet and inverse photoemission spectroscopy (UPS and IPS, respectively) probe a depth comparable to the electron mean free path ( x50 A); is able to detect both occupied and unoccupied states by simply reversing the tunnel bias; is a local technique, capable of imaging single states;

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does not require high-quality oriented films, in contrast to conventional metal-insulator-metal (MIM) tunnel junctions. There is also no electric breakdown, because vacuum is used as a barrier, instead of an oxide, leading to a larger accessible energy range and to less noise and background.

D. Inelastic Tunneling Spectroscopy In the previous sections the discussion was confined to perfect metalvacuum-metal tunnel junctions with sharp, well-defined interfaces. In these systems the electrons pass the potential barrier without energy loss. But what happens when molecules are adsorbed on one of the surfaces? In the first place, there is an effect on the elastic tunneling yield. The presence of the molecule will polarize the substrate, giving rise to an enhancement or a lowering of the LDOS (Lang, 1986a; see Section 1V.C).This resonance has a typical width of 1 eV and can be observed in principle by the techniques mentioned in the previous section. The use of elastic spectroscopy for identification of molecules is difficult because of the broadening and shifting of the original molecular orbits and the limited access to molecular states within the energy region of STM operation. Therefore, a second effect might be more important: inelastic electron tunneling spectroscopy (IETS). Here, internal vibrations are probed via tunneling. These modes are less sensitive to chemi- or physisorption and may be more suited for fingerprinting adsorbed molecules. The process of inelastic tunneling is depicted in Fig. 5. Parallel to the (ohmic) elastic process, electrons can tunnel through the barrier and lose an amount of energy hw by exciting an impurity state. This can only take place when the electrons are raised sufficiently in energy by the applied voltage, so that they can occupy an empty

FIG.5. Principle of inelastic tunneling. When the voltage V between tip and sample exceeds the threshold hR/e, where R is the frequency of a vibrational mode of an adsorbed molecule, an inelastic channel is opened, since the electron can lose energy to this mode and is still able to tunnel into an empty level of the sample. [After Person and Baratoff (1987).]

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level at the other electrode of the junction. In other words, eV 2 hw has to be obeyed. hw is typically on the order of 100 meV. IETS was applied for the first time by Jaklevic and Lambe (1966) in the case of metal-oxide-metal junctions. IETS spectra obtained with solid-state junctions are often difficult to interpret, a result of the ill-defined environment in which the molecules are positioned. A discussion has arisen concerning the extent to which the inelastic process will contribute in a typical STM arrangement. Binnig et al. (1985b)made a first attempt to estimate the effect of inelastic tunneling in STM. They adapted the result for a planar junction to the STM geometry, taking the weak dipole interaction between the tunneling electron and the molecule as the mechanism for excitation. Taking into account the smaller barrier width and height in the STM case, the dielectric constant of 1 for vacuum, and the highly focused tunnel beam, a conductance enhancement of approximately 2.5% was calculated to be caused by the inelastic tunnel channel, assuming reasonable barrier parameters. The same order of magnitude was also found by Persson and Demuth ( I 986). An even larger contribution to the inelastic tunneling in the STM case can be expected from resonant scattering, since the electrons mainly flow from or to the tip via the adsorbed molecule (Persson and Baratoff, 1987; Baratoff and Persson, 1988; Persson, 1988). In this process the electron is trapped temporarily in an orbital of the molecule, thereby exciting the molecule into a vibrational mode. When the electron tunnels out again to the substrate, the molecule is left in this excited state. Another possibility is that the electron absorbs the vibrational quantum again, which leads to a virtual elastic process. The latter process leads to a strong decrease of the conductance because of a strong back-scattering. The total effect can lead to a conductance reduction of 10% or more. Experimentally, the high impedance of an STM junction is a problem. In planar junctions the typical resistance is 100 R, whereas in the STM geometry this is higher by a factor of lo6. This puts severe restrictions on cable capacitances, electronics and modulation frequencies to be used in the detection of the second harmonics. Another problem is the stability of the barrier width in order to detect the small changes in the current associated with the inelastic process:

as derived from Eq. (2). In the case of resonant scattering this implies a barrierwidth stability below 0.01 A.This is attainable with present STM setups. To obtain a high energy resolution the STM preferably should be operated at

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cryogenic temperatures, since the vibrational states are broadened by approximately 5.4 kT (i.e., 150 mV at room temperature). The first experimental observation of inelastic tunnel processes has already been reported. Smith et al. (1986a)observed peaks in d21/dV 2 versus V for a graphite-tungsten system. They attributed the peaks to phonon excitations. Vibrational modes of molecules were observed by Smith et al. (1987a) and van de Walle et al. (1987a). In both experiments, however, the peaks, associated respectively with sorbic acid on graphite and CO on Ni( 11l), were observed in d l / d V versus V. These observations still await an explanation. AND ELECTRONICS 111. CONSTRUCTION

Basically, an STM should be able to control the position of the scan tip with respect to the sample. For this purpose the tip is generally connected to the sample via a U-shaped arm, consisting partly of piezoelectric material. By applying voltages to the piezoelectric elements it is possible to displace the tip in three dimensions with respect to the sample. The movement perpendicular to the sample surface is usually controlled by an electronic feedback system, which keeps the tunnel current between tip and sample constant. The range of tip displacement depends on the application of the instrument but is typically 1 pm3. In general a second position system with a large range is required to bring tip and sample within the range of the former fine-positioning system. Whether the resolution of an STM reaches the theoretical lower limit dictated by the tunnel process (see Sections 1I.A and 1V.A) depends directly on the design of the microscope. Insensitivity to internal resonances, proper isolation from external vibrations, low noise of the electronics and the condition of tip and sample determine the final performance of the instrument. Below we discuss the most important design criteria. A. Mechanical Design 1. Fine Displacement

The requirements for an x - y - z translator are great stiffness and a low mass. In this way a high mechanical resonance frequency is obtained, and consequently the translator’s sensitivity to external disturbances is decreased. Also, the maximum scan speed depends on the resonance frequencies. The frequency of the tip motion parallel to the sample surface should lie below the lowest resonance frequency of the system coupling to this motion. The

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frequency components of the tip motion perpendicular to the surface are generally higher than those of the lateral motion, since they are determined by the roughness of the surface and the scan speed of the tip. Therefore the resonance frequencies coupling to the perpendicular motion should be made as high as possible, e.g., by transporting only a small mass in this direction (Robinson, 1988a). In conflict with these criteria is the need for a large scan range. Increasing the scan range will lead in most cases to a loss of resolution, since an increase of the range of the amplifier or of the sensitivity of the used piezoelectric material will also increase the effect of electrical noise of the amplifiers, and an elongation of the piezoelectric material will lower the stiffness of the instrument. Therefore a compromise has to be made, depending on the application. As mentioned already, in most STMs piezoelectric materials are used for the x - y - z translators. An exception is the large-range STM of Garcia Cantu and Huerta Garnica (1987) which is controlled by coils moving inside fixed permanent magnets. Piezoelectric ceramics can readily be purchased from suppliers such as Philips, Quartz and Silice, Siemens and Vernitron with a large variation in properties and shapes. Many of the designs are based on the original design of Binnig et al. (1982a), consisting of bars that are glued, clamped or machined in the shape of a tripod and fixed to a stainless steel base frame (Gerber et al., 1986; Jericho et al., 1987; Sakurai et al., 1988; Cox and Griffin, 1988). An example is shown in Fig. 6. In some designs the bars are replaced by piezoelectric tubes (Sonnenfeld and Hansma, 1986; Vieira et al., 1987; Chiang et al., 1988a) or metal tubes, connected to bimorph disks (McCord and Pease, 1986; Blackford et al., 1987),enlarging the scan range into the micrometer region. The advantages of such a construction are obvious: It is simple to construct; electrical connections are easily made; the axes are orthogonal, which leads in general to little crosstalk between the x-, y- and z-signals (Park and Quate, 1987a);and there is ample room for attachment of a tip holder. However, resonance frequencies are generally low, being on the order of 3 kHz (see, for example, Demuth et al., 1986a) because of a lack of rigidity. An exception is the tripod of Okayama et al. (1985), machined out of a single piece of piezoelectric material, yielding a resonance frequency of 20 kHz. The asymmetry of the tripod construction also causes a large sensitivity to variations in temperature, which leads to a considerable thermal drift, distorting the images. The drift can be reduced by redesigning the tripod into a symmetric model (Berghaus et ul., 1986; Drake et al., 1986; Davidsson et al., 1988).A further improvement is realized by a careful choice of the construction materials with consideration given to thermal expansion, or by an explicit built-in thermal compensation (van de Walle et al., 1985; Sonnenfeld and Hansma, 1986; Hermsen et al., 1987; Jericho et al., 1987).An example of

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4

Viton VibrationDampers for Wiring

FIG.6. An STM formed by a tripod scan unit and a louse for coarse adjustment. The STM is placed on top of a stack of stainless steel plates with pieces of Viton (not shown) in between for vibration isolation. The Vit.on dampers on the side of the plates are used to lead the wires from stage to stage in order to damp vibrations that couple in through the wires. [After Gerber rt al. (1986).]

thermal compensation in three directions is shown in Fig. 7. Such modification can even improve the stiffness of the construction, yielding resonance frequencies of 20-30 kHz (Bando et al., 1988; Gregory and Rogers, 1988). The above-mentioned construction typically have a sensitivity of 5 A/V, which leads to the use of high-voltage amplifiers to reach a scan range of about 2500 x 2500 x 2500 A3. Larger scan ranges can be obtained by using bimorphs, since they offer a large deflection at low voltages. This is achieved at the cost of stability, unless the construction is such that the deflection range is comparable to that of the tripod (Pohl, 1986). A complete bimorph STM was built by Muralt et al. (1986a).In spite of the low operating voltage (120 V), the range is 8 x 8 x 8 pm3.A similar construction was developed by Matey et al. (1987) and Heil et al. (1988).Bimorphs are very well suited for use at low temperatures, as is proven by a design by Burger et al. (1989) that has a range of 5 x 4 x 17.5 ,urn3 at 4.2 K.

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(a)

171

(b)

FIG.7. Scan unit with thermal compensation in three perpendicular directions. All parts are of stainless steel or aluminum, except the cross-hatched parts, which are of piezoelectric material; the arrows indicate their polarization. (a) Side view. The thermal expansion of the piezoelectric z-drives (2) is compensated by the expansion of the drives (7). Tunnel-current control occurs via the drives (2) (fast response due to the low-mass transport). (b) Front view. The thermal expansion of the drives (4) and (7) is canceled by the expansion of the drives (2) and ( 6 ) .The symmetrical design also diminishes temperature effects. Lateral motion of the tip is realized via the inner drives in combination with the outer drives. [After Hermsen e l a/. (1987).]

A stiff large-range scan unit can be constructed out of a single piezoelectric tube, radially polarized (Binnig and Smith, 1986). Tip motion in three orthogonal directions is made possible by a special shape of the electrodes on the tube. On the outer side is a cylindrical quadrant of electrodes, and on the inner side is a single electrode. If a voltage is applied to one of the outer electrodes, this part of the tube will expand or contract, resulting in a bending of the whole tube and a lateral motion of the tip. The axial motion is realized by a voltage on the inner electrode or by a voltage to all outer electrodes. In the latter method the inner electrode can be grounded, which automatically provides a shielding of the tip wire when it is led through the tube center (Besocke, 1987; Lyding et al., 1988a). The sensitivity of tubes varies from 20 to 100 A/V (Besenbacher et ul., 1988; Snyder and de Lozanne, 1988) and is usually greatest for the bending directions. The resulting large scan range is especially suitable for imaging extended structures-for example, in biology and (e1ectro)chemistry (Sonnenfeld et ul., 1987; Dovek et a/., 1988a; Emch et al., 1988a). A tube STM is also very convenient for operation at cryogenic temperatures because of the possibility of compact design and because the sensitivity at 4.2 K is comparable to that of a conventional tripod STM at room temperature (Smith and Binnig, 1986; Fein et al., 1987). The rigidity of constructions based on tubes is large, since very compact designs are possible (Albrektsen et al., 1989; Anselmetti et ul., 1988a; Bando et al., 1988), resulting

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in resonance frequencies of approximately 10-60 kHz and 40-100 kHz for modes perpendicular and parallel, respectively, to the tube axis. Combining this with the use of low-noise low-voltage amplifiers leads to highperformance STMs. Also, the thermal stability is good, because of the symmetric design when the tip is positioned on the tube axis. For the axial motion, thermal compensation is possible with the application of a concentric double-tube system (Besenbacher et al., 1988; Lyding et al., 1988a; Snyder and de Lozanne, 1988). The main disadvantage of a tube scanner is the inherent crosstalk between the x, y and z motion, since the scan unit consists of only one part. First-element calculations on the bending of such tubes by Carr (1988) give information on the sensitivity and the crosstalk. Another source of crosstalk arises from the asymmetric activation of the tube in the case of lateral motion, as described above. This can be compensated for by mounting the tip also asymmetric or by a posteriori subtraction of a background plane from the data. The best solution is of course an antisymmetric activation of the tube by applying opposite voltages to opposite outer electrodes (Besocke, 1987; Fein et al., 1987; Besenbacher et al., 1988; Lyding et al., 1988a). This also doubles the scan range in the bending directions. Another compact scan unit has been designed by Anders et al. (1987), who used a single 10-mm diameter piezoelectric disk with specially shaped electrodes for orthogonal tip movement in a cylindrical coordinate system. The approach of Uozumi et al. (1988) consists of one standard thicknessdeforming piezoelectric plate and two shear-deforming piezoelectric plates, polarized in perpendicular directions and stacked on top of each other, thereby yielding an extremely high resonance frequency of 200 kHz.

2. Coarse Displacement One of the necessary elements in a piezoelectric-driven microscope is a mechanism to bring the distance between the tip and the sample surface of interest within the operating range of the x-y-z scan unit. In most designs the sample stage is subject to this coarse translation, whereas the tip unit is mounted to the fine control, which is fixed to the base frame. This means that the coarse translator must bring the sample over a distance of a few millimeters into a close approach to the tip, with a minimum displacement below the maximum scan range of the tip. To choose different parts of the sample, one or two more degrees of freedom for coarse positioning is desirable. O n the other hand, the sample stage should be connected to the tip scan unit as rigidly as possible in order to minimize the influence of vibrations. One option is the use of a remotely controlled coarse positioning. This guarantees minimal influence of external disturbances since mechanical contact with the outer world is not necessary. This approach was first taken by

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Binnig et al. (1 982a), who developed a piezoelectric walker, generally referred to as a “louse”. It consists of a thin piezoelectric disk, a few centimeters in diameter, which is supported by three or four metal feet with a thin dielectric coating. The assembly is placed on a polished metal base plate (see Fig. 6). The louse can take steps when some of its feet are clamped electrostatically to the base plate, thereby contracting the disk, and the remaining feet are then clamped under expansion of the disk. Typical step sizes lie between 0.1 and 100 pm, and the step rate can easily attain 50 Hz. The principle of the louse is used by many researchers (Mamin et al., 1985; van de Walle et al., 1985; Berghaus et al., 1986; Gerber et al., 1986; Tokumoto et al., 1986; Blackford et al., 1987; Chiang et al., 1988a). For optimum stability the sample stage is usually not mounted on the piezoelectric disk but rather on one of the feet, on a frame resting on the feet, or on a separate foot loosely coupled to the louse (Blackford et al., 1987). The major problem with piezoelectric walkers is the small electrostatic clamping force. Little irregularities on the sliding plane, such as dust particles, may already obstruct the motion of the walker. A louse that is not dependent on electrostatic forces can be realized by using a double set of piezoelectric feet, each set able to stick onto or glide above the base plate by elongation or contraction, respectively, thereby making real steps (Binnig and Gerber, 1980; Uozumi et al., 1988). Other designs, with less resemblance to a louse, use a bimorph (Kaiser and Jaklevic, 1986) or an inchworm-like construction (Hermsen et al., 1987), the latter being able to displace the whole scan unit. Gregory and Rogers (1988) also use an inchworm. Smith and Elrod (1985) suggest the use of the much stronger electromagnetic force between a permanent magnet and an electromagnet to drive the sample stage. Corb et al. (1985) and Tokumoto et al. (1986) also followed this approach. Even commercially available stepping motors are used for the coarse motion (Park and Quate, 1987a; Dovek et al., 1988a). Another method based on piezoelectric material but less sensitive to dust takes a dynamic approach (Anders et al., 1987; Pohl, 1987). A piezoelectric element is expanded and contracted in a sawtooth-like way. During the slow expansion the sample stage on top of the piezoelectric element follows this motion, whereas during the fast contraction it slips over its support. This leads to a steplike motion of the sample stage in one or two dimensions. Coarse motion in the vertical direction can be obtained in a similar way (Anders et al., 1988). The same trick is applied in the designs of Besocke (1987), where the sample is positioned above the tip, resting on three piezoelectric tubes. By sawtooth-like bending of the tubes, a lateral sample motion is induced. Since the tip is mounted on a similar tube, the design is thermally compensated. Emch et al. (1988b) and Guckenberger et al. (1988) also built a microscope on this principle. The same idea can be realized by placing the sample stage on

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Viton stack

FIG.8. Principle of dynamical coarse adjustment of the sample- tip distance using an idea of Besocke (1987). The sample is attached to the ramp sample holder and placed on top of three piezoelectric tubes. When a sawtooth voltage is applied to the tubes, such that the tubes bend in a tangential direction, the sample holder is set in a steplike rotational motion. The ramp on the sample holder transforms the rotation into a vertical translation. The tube in the center forms the scan unit of the tip. The construction is thermally compensated in the vertical direction. [After Michely et al. (1988).]

top of a single piezoelectric tube, concentric with the tip tube (Besenbacher et al., 1988; Snyder and de Lozanne, 1988).A slight modification of the above systems also makes tip-sample approach possible (Lyding et al., 1988a; Michely et al., 1988).The principle is demonstrated in Fig. 8. Instead of using remotely controlled positioners, the coarse displacement can be done by hand or by motor by making a direct coupling to the outer world. Because of the direct transmission of force, the coarse positioning is in general much stronger, allowing for a more rigid connection between the sample stage and the tip unit via a clamping or a spring-loading mechanism. This also implies that the tip unit can be subjected to the coarse motion, instead of the sample stage. A disadvantage is the restricted decoupling from the environment during positioning. Therefore the sample stage can often be disconnected from the coarse adjustment during STM operation-for example, via a retractable piezoelectric actuator (Burger et al., 1989).

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Usually a rotary motion has to be transferred into a translational motion. A fine-pitch screw or a differential micrometer screw are normally used for this purpose, yielding positioning within 10 pm or 0.1 pm, respectively. The differential screw can be used without further displacement reduction if the range of the scan unit is large enough (Bando et al., 1988; Burger et al., 1989; Dovek et al., 1988a). Often, however, a more accurate positioning is desirable. If the sample stage is attached to a spring-loaded lever near the pivot and the (differential) screw is placed at the opposite site, the movement of the screw can be reduced by a considerable amount (Coombs and Pethica, 1986; Demuth et al., 1986a; McCord and Pease, 1986;Jericho et al., 1987; Kaiser and Jaklevic, 1987; Sonnenfeld et al., 1987; Cox and Griffin, 1988; Pashley et al., 1988a; Sakurai et al., 1988). Differential springs or membranes, where the motion is reduced by a set of (leaf) springs or membranes of various stiffnesses, are also used (Smith and Binnig, 1986; Fein et al., 1987; Hermsen et al., 1987; Albrektsen et al., 1989; Anselmetti et al., 1988a; Besenbacher et al., 1988).

3. Piezoelectric Materials and Calibration As is clear from the previous paragraphs, piezoelectric ceramics are essential in the construction and operation of an STM. The effect used in STM is called the inverse piezoelectric effect, i.e., the induction of strain when an electric field is applied. To a first approximation, the expansion (or contraction) of the material behaves linearly with respect to the applied voltage. The relevant parameter used by the suppliers is the piezoelastic voltage constant d,, giving the induced strain si in direction i per unit electric field E j in the direction j of the polarization of the piezoelectric material:

in the absence of mechanical stress. Typical values of d , range from 2 to 6 A/V. In most STM applications only d31 is of importance. For a bar (length I, thickness d ) the elongation is A1 = d 3 , ( l / d ) V . The axial motion of a tube (length I, thickness d, radius r) is the same as for the bar; the bending motion yields A x = (1/2r)Al = d,,(l2/2dr)V (Locatelli and Lamboley, 1988). The bending of a bimorph (length 1, thickness d ) is described by A x = d 3 , ( 3 1 2 / 8 d 2 ) V(Pohl, 1986). Unfortunately, piezoelectric materials also have some drawbacks that may affect the STM performance: Aging with a logarithmic decrease in polarization. An extra aging effect occurs after regular bake-out or with the application of high electric fields in a direction opposite to the polarization. Especially, material with a high d factor is relatively unstable in time and in temperature because of the low

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Curie point. Materials with a low Curie point can be regenerated easily, however. Temperature dependence of the d factor. As temperature is lowered, the voltage constant decreases drastically, with a factor 2 to 4 at liquid-He temperature (Vieira, 1986; Nishikawa et al., 1987; Simpson and Wolfs, 1987; Viera et al., 1987). This hinders applications in a cryogenic environment. Hysteresis, which can be as great as 10%of the total expansion. It becomes evident when the tip is scanned back and forth along the surface, leading to considerably different images at steep corrugations of the surface (Nishikawa et al., 1987). The hysteresis can be minimized by a proper choice of material, and by adding a small capacitor in series with the piezoelectric element (Kaizuka and Siu, 1988), or by controlling the charge on the electrodes of the piezoelectric transducers instead of the voltage difference (Newcomb and Flinn, 1982). Creep, i.e., the slow response additional to the instantaneous expansion to an applied voltage. It is one of the causes of drift and tip displacement between successive measurements. Creep extends over minutes in a logarithmic way and depends on the temperature (Vieira, 1986). It can be diminished by using piezoelectric single crystals with low defect concentrations. Despite all the drawbacks, piezoelectric ceramics are still the best alternative for remotely controlled subnanometer positioning in STM applications. Considering the growing interest in STM together with the increasing research efforts in astronomy, where piezoelectric material is used for the adjustment of mirrors and parabola antennae, the future will certainly bring piezoelectric materials with improved characteristics. After an STM has been constructed, it is essential for a safe interpretation of the recorded data that the displacement versus applied voltage be calibrated. For this purpose several methods can be applied. The most direct way is to observe with the STM a regular atomic surface structure and calibrate the piezoelectric elements accordingly. For calibration of the zdirection, a known monoatomic step can be used. The piezoelectric activity can also be tested very sensitively by measuring capacitive changes with a nulldetecting capacitance bridge (Yurke et al., 1986; Vieira, 1986), yielding an accuracy of 0.1-0.01 A. Other possibilities are the use of optical interferometry (500 nm resolution), inductive sensors (0.1 pm resolution), mechanical sensors (Locatelli and Lamboley, 1988) or observation by a scanning electron microscope (SEM). 4. Vibration Isolation

Proper isolation of the STM from disturbances of the outer world is of crucial importance for the ultimate resolution of the images. The two main

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sources of disturbance are the building and sound. Buildings typically vibrate at frequencies between 5 and 100 Hz, with major peaks around 25 Hz, originating from floor resonances, pumps and generators. The amplitude of the floor vibrations can in some cases reach values of several microns. This means that a reduction by a factor of lo5 has to be achieved in order to come to a vertical resolution of 0.1 A. As mentioned already in Section III.A.l, vibration isolation is less important when the stiffness of the STM itself is great. Pohl(l986) and Okano et al. (1987) investigated the response of an STM to external vibrations by representing the lack of rigidity by a stiff spring between sample stage and tip unit (see Fig. 9a). When the external vibrations are coupled to the sample stage, the response of the STM can be obtained by monitoring the oscillations in tip-sample distance. It turns out that the STM behaves like a high-pass filter: At high frequencies, above the cutoff frequency of the spring-tip unit system, all vibrations couple directly to the tip-sample distance, whereas at low frequencies the response increases roughly by 12 dB/octave. At the cutoff frequency, the response shows a resonance peak. This shows that external vibrations should be well below the cutoff frequency of the STM and confirms the advantage of great stiffness for an STM. A second measure to diminish the effect of vibrations is to optimize the environment of the microscope by situating the whole experimental setup in a

-

ANTIVIBRATION TABLE

-l2O01

10

1

100

1000

"/Wi

(a)

(b)

FIG.9. (a) Simplified model of an STM in combination with a vibration isolator. The lack of stiffness of the STM is described by a spring between tip unit and sample stage. External vibrations are passed on to the sample stage via the springs of the isolation. (b) The transfer function ( I ) for the vibration isolation acts as a low-pass filter with a resonance at the eigenfrequency of the isolation w , . The response of the STM to vibrations of the sample stage (11) acts as a high-pass filter with a resonance at the eigenfrequency of the STM. The combined response of the STM to external vibrations (111) shows a plateau between the two resonances. [After Okano et al. (1987).]

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quiet part of the laboratory-for example, in the basement, in a wooden box filled with sand (Blackford et al., 1987; Fein et al., 1987; Jericho et al., 1987) or on an air-bearing table or legs (Demuth et al., 1986b; Fein et al., 1987; Kaiser and Jaklevic, 1987). Sound isolation also improves the instrument (Coombs and Pethica, 1986). Operating the instrument at quiet times when traffic inside and outside the building is less intense is preferable. The third measure is to shield the STM from external disturbances by sufficient vibration isolation. This can be done by suspending the STM on coil springs (e.g., Snyder and de Lozanne, 1988). For atmospheric STMs, bungee cords are also used. The springs act as a low-pass filter: no influence below cutoff, whereas above the cutoff frequency the response decreases by roughly 12 dB/octave. Thus a low cutoff is desirable, and it can be attained by using soft springs and a heavy load. Typical cutoff frequencies are around 2 Hz. At the cutoff frequency a resonance peak occurs. This peak should be suppressed by adding damping to the system. Damping also leads to faster fading of already-present vibrations. However, too much damping will lead to a reduction of filter performance at high frequencies, since any form of damping “connects” the microscope more to the environment (Okano et al., 1987).An often applied method for damping is the use of Viton links in series with the springs. The Viton will also absorb higher frequencies. In the case of a stable STM, Viton isolation alone may be sufficient (Besenbacher et al., 1988). Another method uses good conductors, connected to the STM stage and positioned in a permanent magnetic field. Damping of vibrations is realized by inducing eddy currents in the conductors, which dissipate energy. Following again the approach of Pohl(l986) and Okano et al. (1987), the response of an STM is the product of its internal high-pass filter and the lowpass action of the external isolation. This leads to a constant plateau in the response between the cutoff frequencies of both filters, beyond which the response decreases (see Fig. 9b). The response level of the plateau depends on the separation between the cutoff frequencies, yielding a response of approximately (1/40)”,n being the separation in number of decades. To attain the above-mentioned reduction factor of lo5, n should be at least 3. Often double-stage spring systems are used, since more stages increase the filter performance at higher frequencies (Park and Quate, 1987b; Chiang et al., 1988a; Sakurai et al., 1988). Best performance is acquired if only the second stage is damped (Okano et al., 1987). A very compact vibration-reduction stage was designed by Binnig et al., (1984b).A small STM is placed on a stack of several stainless steel plates that are separated by small Viton dampers. Because of the differences in weight carried by the successive dampers the complete stack serves as a multiplefrequency filter. Because of the great stiffness of Viton, more than five stacks are necessary for good performance (Okano et al., 1987).A typical resonance frequency is 16 Hz. The unit easily fits onto a vacuum flange and is therefore

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179

HIGH VOLTAGE I DAI

X

I

DIFF.

FILTER

-

"t 7$

FIG.10. Schematic representation of STM operation. The lower half depicts the feedback loop to maintain a constant tunnel current between sample and tip. The upper half represents the external control for scanning and data acquisition.

very convenient to use. The use of such units is very common now (Gerber et al., 1986; Chiang et al., 1988a; Cricenti et al., 1988; Dovek et al., 1988a).An example of a stack is shown in Fig. 6. B. Electronics and Data Processing

A basic and essential ingredient in tunneling microscopy is the electronic control of the piezoelectric elements and acquisition and processing of the data. Here a division into two components can be distinguished: electronics for the (internal) feedback control of the vertical tip position, and those for the (external) control of lateral tip position and data flow (see Fig. 10). The first part is relatively straightforward and consists merely of basic electronic components readily available. The second part, mainly computer-controlled, has become very complex over the years because of the increasing amount of information extracted from the tunnel signal. 1. Feedback Electronics In general terms, the feedback electronics consist of the following parts: A high-stability voltage source with a range between - 5 and + 5 V and which is capable of superposition of ac and dc output signals.

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A current detector for sensing and amplifying the small tunnel signals, which are in the range of 0.1 to 10 nA. In general the current is detected via a highohmic resistor, typically 1 MR, across which the voltage drop is detected by low-leakage high-impedance operational amplifiers. The detector can be placed at the low-voltage side (see, for example, Blackford et al., 1987; Park and Quate, 1987a; Besenbacher et al., 1988)or at the high-voltage side of the tunnel barrier (see, for example, van de Walle et al., 1985).The latter has the advantage that one of the electrodes can be grounded explicitly, which may reduce the noise and the occurrence of ground loops. For dc applications both designs pose no problems, although the small signals require a good shielding. Therefore the current detector is sometimes positioned close to the tunnel barrier, such that an amplified signal is transported to the rest of the electronics (Park and Quate, 1987a; Robinson, 1988a). When a small ac modulation is applied (for spectroscopic measurements, see Section II.C), the modulation frequency is limited by the capacitance of the tunnel junction (typically 0.1 pF), parallel to the tunnel resistance (typically 1 GO), yielding rather low cutoff frequencies ( x 1.5 kHz). When the detector is placed in the high-voltage line, an additional capacitance of the coaxial signal wire plays a role, unless a guarding circuit is used, keeping the shielding of the coaxial wires at the same potential as the inner wire. Often a logarithmic amplifier is included in the feedback control to linearize the exponential behavior of the tunnel junction (Fein et al., 1987; Kajimura et al., 1987; Park and Quate, 1987a). A differential operational amplifier to compare the tunnel current with a preset value. The error signal is then fed to an integrator that gives a high dc gain ( x 1000 x ). In this way the difference between set point and actual tunnel current is kept minimal over the entire feedback operating range. The gain at higher frequencies is kept as high as possible without causing oscillations. An additional low-pass filter can increase the total gain and thereby the response time in some cases (Pohl, 1986; Park and Quate, 1987b). Very suitable for this purpose is a variable-gain, low-noise amplifier with adjustable low-pass filter characteristics, since the total gain and frequency range of the feedback loop are strongly dependent on the condition of tip and sample. At this point the signal is fed simultaneously to a high-voltage amplifier that drives the piezoelectric z-drive and a data-acquisition station, which can be a computer, an x-y recorder or a storage oscilloscope. The high-voltage amplifiers that drive the piezoelectric actuators can be purchased from several suppliers, but with the trend to a higher sensitivity for the piezoelectric drives there is less need for high output voltages. This makes

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home-built equipment with tailored performance ( f 150 V with a high frequency range and a low ripple) very attractive. The feedback control described above is suitable for STM operation in the constant-current feedback mode (see Section 1I.A).It was developed by Binnig et al. (1982a) and described in more detail by van de Walle et al. (1985), Pohl (1986) and Drake et al. (1986). The maximum scan frequency is limited to approximately 10 Hz by the mechanical action of the z piezoelectric drive (Coleman et al., 1985; Park and Quate, 1986).This limitation is relaxed in the current-imaging mode (see also Section 1I.A) to scan rates of approximately 1 kHz (Bryant et al., 1986a),which results in less distorted images by reducing drift and low-frequency noise. For spectroscopy the electronics need only minor changes. Spectroscopy with ac modulation (see Section 1I.C) is comparable to the case of solid-state junctions. To avoid singularities around V = 0, the feedback can be changed to control the tunnel resistance instead of the tunnel current (Elrod et al., 1984). Spectroscopy according to current-imaging tunneling spectroscopy (CITS) is more difficult. The electronics for CITS is extensively described by Schroer and Becker (1986),Fein et al. (1987) and Park and Quate (1987a).The I-V characteristics at each tip position can be obtained at a rate on the order of 2 kHz, since the charging time of the cable and stray capacitances is governed by the low substitution resistance of the current detector and not by the tunnel resistance (as in the case of ac modulation). 2. Data Handling and Image Processing For the control of external parameters such as scan width, rate and direction and for data acquisition, handling and representation, most researchers nowadays use computers. In special cases (e.g., real-time fast imaging) function generators with memory oscilloscopes and video cameras are also used. In the case of computer-controlled processing, a personal computer is often used for the actual STM control, for both the coarse displacement and the actual imaging. Several concepts of STM automation have been described in the literature, most of them based on an IBM PC (Aguilar et al., 1986; Schroer and Becker, 1986; Bapst, 1987; Becker, 1987; Park and Quate, 1987a).Via 12- or 16-bit D/A converters, the tip is scanned along the surface, and the feedback signal or derivative signals are acquired via A/D converters. The use of 16-bit converters makes possible high resolution of both large and small areas, which makes zooming possible (Bapst, 1987).A simple display of the measured data is often available during the measurements, e.g., by display during the trace-back of the tip (Aguilar et al., 1986). These displays involve quasi-three-dimensional line plots and top-view grey or color plots. Histograms of the grey or color scales simplify the setting of the

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grey or color levels. To optimize the display of the data, subtraction of a background plane or a hyperbolic paraboloid (Rosenthaler et al., 1988) is desirable. Statistical differencing can be applied to enhance or reduce the corrugation or steps in part of the image (Wilson and Chiang, 1988). More elaborate image processing on a mainframe or work station leads to (real-time) perspective solid modeling of the data with flat or Gouraud shading (Rosenthaler et al., 1988). Height plots with contour lines also can be calculated. Remodeling of the surface is sometimes necessary to compensate for drift during the image acquisition; this is performed by a least-squares fit to the supposed underlying lattice structure. Postprocessing of the STM images is easily performed with powerful computers. Many filtering techniques are available to diminish the noise, such as smoothing, median filtering, (Laplace) sharpening, edge detection and correlation averaging (Soethout et al., 1988)in the spatial domain, and Wiener filtering (Stoll and Marti, 1987) and Weiner filtering (Park and Quate, 1987c) in the frequency domain (by two-dimensional fast Fourier transformation (FFT) of the data). C. Tip Preparation and Characterization

The understanding of the resolution of the STM and the interpretation of its images are closely related to the knowledge of the atomic structure of the probing tip. In the first years of tunneling microscopy, little attention was given to this subject. The recipe to get a tip that would give atomic resolution was a matter of trial and error. Several procedures were known to give high resolution, but the physics behind it was lacking. Since then, some progress has been made in the preparation and characterization of STM tips. The tip material commonly used for vacuum applications is W. Wires are preferentially (1 10)oriented, leading in general to good results. Single-crystal tips of (100) (Kuk and Silverman, 1986) and (1 11) orientation are also used. The latter orientation might be advantageous because of its large activation energy for surface diffusion (Neddermeyer and Drechsler, 1988; Nishikawa et al., 1988). For application in air or liquid, Pt and Pt-Ir wire is more convenient since W easily oxidizes. The wire diameter typically is 0.1- 1 mm. Thick and short tips are preferable for their high resonance frequency. If the STM is operated in an electrochemical environment, a coating around the tip (except for its apex) is applied, usually made of glass (Heben et al., 1988). The tip preparation starts with a rough sharpening of the wire. Common techniques are grinding, polishing and cutting with scissors or pincers, often followed by electrochemical etching (Bryant et al., 1987; Michely et al., 1988;

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FIG. 1 I. Preparation of a monoatomic tip, observed via FIM imaging. (a) Trimer created by field evaporation. (b) Monoatomic tip after deposition of W atoms onto the tip. (c) Superposition of (b)and the image obtained after removal of the extra atom. Additional atoms next to the trimer are now visible. Copyright 1986 by International Business Machines Corporation; reprinted with permission. [After Fink (1986).]

Nicolaides et al., 1988). Also, a brittle tip such as silicon (Anders et al., 1988) or pencil lead (Colton et al., 1987) can be broken. When the tip is mounted inside the STM, several additional treatments may improve the resolution. These methods are based on an uncontrollable exchange of material between tip and sample or a rearrangement of the tipfor example, by melting (van de Walle et al., 1986). The sample may be locally damaged during this preparation; thus, another sample area for measuring is necessary. Some methods of sharpening include a temporary increase in the tunnel current (de Lozanne et al., 1985), application of a high electric field (>I00 V) for some minutes (Binnig and Rohrer, 1983), field emission during scanning (Berghaus et al., 1987a; Wintterlin et al., 1988), electron bombardment (Demuth er al., 1986b; Chiang and Wilson, 1986) or contact between tip and sample by hand or under electronic control, by an induction pulse (van de Walle et al., 1986) or by oscillation of the feedback. In UHV, a very precise technique of tip modeling involves field evaporation and deposition under FIM control. Fink (1986) was the first to show the possibility of layer-by-layer growth or removal resulting in pyramidal tips with a single (ad)atom at the apex (see Fig. 11). Several groups have now integrated FIM in their STM design for in-situ characterization of the STM tip (Kuk and Silverman, 1986; Michely et al., 1988; Nishikawa et al., 1988; Sakurai rt al., 1988). FIM analysis of tips also led to new recipes for STM tip preparation. Binh and Marien (1988) and Binh (1988) found that annealing at high temperature, eventually in an oxygen atmosphere, gives good results. The quality of STM tips can also be estimated from SEM and TEM images (Chiang and Wilson, 1986; van de Walle et al., 1986), although this might be deceptive (Nicolaides

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et al., 1988). These observations led to new recipes based on ion milling (Biegelsen et al., 1988; Tiedje et al., 1988). Finally, the tip shape can be investigated with STM itself by probing indentations in a flat soft surface that have been made by gently pushing the tip into the surface (van de Walle et al., 1986).

D . Operating Environments The first STMs were operated in vacuum, but upon improvement of the technique it became clear that operation with good results would also be possible in a gas atmosphere such as ambient air, at low (cryogenic) temperatures, and in liquids. These different environments will require specially adapted STMs, which are briefly described below. 1. Ultrahigh Vacuum The STM should be constructed from low-outgassing materials such as stainless steel, aluminum (oxide) and Macor. Piezoelectric materials pose no problem but limit the bake-out temperature of the UHV chamber to well below the Curie point. The STM should be assembled by clamping (Davidsson et al., 1988),or by using special glues such as low-outgassing epoxy. For wire insulation, polyimide is convenient. The coarse displacement was originally performed by remotely controlled walkers, but in general it has been taken over by direct motion via rotary feedthroughs. However, mechanical coupling between the STM stage and the UHV chamber should be minimized-for example, by the application of bellows. A viewport in combination with an optical microscope is handy for proper positioning of sample and tip. Mechanical damping can be performed with Viton, provided that the maximum bake-out temperature is restricted to 150°C. Eddy-current damping should be applied with care since stray magnetic fields may influence other analysis techniques (Park and Quate, 1987a). The advantage of operating the STM under UHV conditions is the use of clean and well-defined samples and tips. The tips can be formed by the methods of the last section and characterized by FIM, SEM or TEM. Also, the ability to replace a tip without breaking the vacuum is desirable. Therefore some STM designs include the possibility of in-situ tip exchange or even replacement of the scan unit (Chiang et al., 1988a; Cox and Griffin, 1988; Davidsson et al., 1988; Emch et al., 1988b). Also, the sample can be taken out of the STM in most cases (Park and Quate, 1987a; Chiang et al., 1988a).This enables the exchange of samples and offers the possibility of sample treatment and characterization. Ion sputtering and annealing by resistive heating and electron bombardment are generally

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applied cleaning techniques. For characterization of the samples, LEED and AES are normally available. Some researchers have built their STM inside an SEM, capable of positioning the tip above specific sample spots (Gerber et al., 1986; Ichinokawa et al., 1987; Anders et al., 1988; Vazquez et al., 1988). 2. Gas Atmosphere The STM should of course be inert for the surrounding gas. Special attention should be paid to proper isolation against vibrations and against thermal influences, since the coupling is more direct than in the UHV case. It is especially preferable to protect the STM against sound by placing it in a damping box. A fast sample and tip exchange is advantageous to minimize degeneration due to causes such as oxidation. A proper design also gives easy access to the tip-sample region by an optical microscope (Emch et al., 1988a; Guckenberger et al., 1988).

3. Low Temperature The STM design should take into account the diminished piezoelectric activity at low temperatures (approximately a quarter of the activity at room temperature). Bimorph (Burger et al., 1989) and tube STMs (Smith and Binnig, 1986; Fein et al., 1987; Lyding et al., 1988a) are favored. Temperature compensation is advantageous for short stabilization times when the STM is operated at varying temperatures. Eventually it will be possible to perform the coarse adjustment at room temperature, enabling a compact design (Lyding et al., 1988a). The STM, mounted at the lower end of an insert surrounded by boiling liquid, is subjected to large vibrations. Vibration isolation by using springs or levers is awkward at cryogenic temperatures and may lead to warming caused by dissipation (Burger et al., 1989). The use of a rigid STM is therefore recommended, in combination with a stable support of the insert and isolation of the whole Dewar from the environment. The latter is realized, for instance, if the Dewar is placed in a wooden box filled with sand and joined by a flexible connection to auxiliary equipment such as pumps (Fein et al., 1987). Another problem involving the length of the insert is the wiring, which can lead to excessive cable capacitance. A possible solution would be to place the current-sensing circuit close to the junction inside the Dewar. 4. Liquid STM in liquids can be advantageous for certain experiments. Biological substrates can be investigated in a natural environment. Chemical reactions (such as catalysis) and electrochemical reactions can be monitored in situ. To

15cm

1

bias wire

RTV insulation

*

, , ' \brass tip

FIG.12. Schematic STM setup for electrochemical application. The scan unit, based on a piezoelectric tube, is shown in the inset. The coarse displacement is done with a stepper motor. The liquid is contained in a glass beaker, placed on a modified Viton stack for vibration isolation. [After Dovek et al. (1988a).]

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L. L. SOETHOUT et al.

ensure compatibility with most electrochemical solvents, it is common practice to use inert materials and to submerge only the tip and the sample into the solution (Dovek et al., 1988a; see also Fig. 12). Tunneling in an electrolytic solution gives rise to the tunnel current, and also to a faradaic current, caused by ionic conduction, which can easily be larger than the tunnel current. If tunneling is carried out at moderate voltages and the tip is coated with a polymer or glass, a stable feedback signal is obtained (Drake et al., 1986; Sonnenfeld and Schardt, 1986). For performing controlled electrochemical reactions, three-electrode voltammetry is normally applied. The true potential of the sample (called the working electrode) is controlled with respect to a reference electrode, while the electrochemical current flows between the working and a counter (or auxiliary) electrode. The potentials are controlled by a potentiostat. In the case of STM, the tip forms a fourth electrode, the voltage of which should also be controlled with respect to the reference. This four-electrode setup (bipotentiostat) is used by several groups, who observe proper operation of the STM even during faradaic-current flow between working and counter electrode (Hottenhuis et al., 1988; Itaya and Tomita, 1988; Robinson, 1988b). IV. THEORY A . Simple Model

The STM is based on the quantum mechanical tunnel effect. In general, tunneling is the transition of a particle from one (metastable) state to another state, both states separated by a classically forbidden region, the barrier. This transition is possible because of the wave character of quantum mechanical states. In the case of STM, the particles are electrons that tunnel between two electrodes, the tip and the sample, which are separated by a potential barrier that in most cases is a vacuum. If no potential difference is applied between the two electrodes, the tunneling of electrons from the tip to the sample is balanced by the tunneling in the opposite direction, resulting in a zero net tunnel current. In the case of an applied voltage, there is an asymmetry between the empty electron states on one side and the occupied states on the other side, resulting in a net current flow. In the simplest picture of STM, the tunnel current I is taken from onedimensional tunneling through a square barrier (see, for example, Kane, 1969), as sketched in Fig. 13. In the three regions of space, 1 and 2 being the electrodes and 3 being the barrier, the Schrodinger equation has to be solved. When an incoming wave from the left, with wave vector kl,, is assumed, the general

SCANNING TUNNELING MICROSCOPY

R2

R3

R1

189

10 -K-1 ----

FIG. 13. Schematics of the one-dimensional square-barrier tunnel junction. The potential of electrode 2 is V above the potential of electrode 1. Only incoming electrons with an energy E between E,, - eC‘ and E , , are able to tunnel from electrode 1 to 2.

solutions are

11/,

=

t+h3 = c(- exp( - KZ)

11/,

+ A,exp(ik,,z);

A,exp(-ik,,z)

+ u+ exp(Kz);

= A , exp( - ik2=z).

(9)

Box normalization of the incoming wave implies IAi12 = 1/L,L being the width of electrode 1 . Energy conservation implies that

k f Z= 2m/h2E K’

kiz

= 2m/h2(U - E ) =

2m/hZE,,

where E is the energy of the incoming electron and U is the height of the barrier, both relative to the bottom of the conduction band of the left electrode, and E , = E + AU = E + &2 - EF, + el/ is the energy of the transmitted electron, relative to the bottom of the conduction band of the right electrode. E,, and E,, represent the Fermi levels of both electrodes. By matching the wave functions on the barrier boundaries at z = 0 and z = s and assuming strong attenuation, the amplitude of the transmitted wave can be calculated. The current density in the right electrode becomes j Z z = -(eh/m)Im

(11/*

2%)

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L. L. SOETHOUT et al.

where jlz= (eh/rn)klZ(Ail2 is the incoming current density and T ( E ) is the transmission coefficient, T ( E )=

16k1,k2,~2

(kf,

+ x2)(k:, + I C ~ exp( )

-

2~s).

The energy dependence is implicit via k,,, k,, and IC according to Eq. (10).At zero temperature only electrons with an energy between E,, - eV and E,, are able to tunnel, so for small bias voltage the transmission coefficient T can be taken to be constant:

where k,, and k,, are the Fermi wave vectors of both electrodes and I C = ~ [2rn/h2+]”’, being the barrier height relative to the Fermi level ( = U - E,,). The total current density, equal to the total current in the one-dimensional case, is found by summing over all incoming waves within the energy window, taking into account spin degeneracy:

+

= 2(eh/rn)

1’2 k,,T(E)

where the prime indicates summation or integration over waves with an energy between E,, - el/ and EFl. Substitution of Eq. (13) yields the total tunnel current I , which is linearly dependent on bias voltage I/ and exponentially dependent on distance between the electrodes s: I/V cc exp( - 2 1 ~ ~ s ) .

(1 5 ) If it is assumed that the above equation can be used also in an STM geometry, the topographic resolution of the instrument can be estimated. There are three important criteria. THE VERTICALRESOLUTION.For typical barrier heights (or, equivalently, work functions) of 4 eV, rc0 N 1.0 A-’. This means that the tunnel current decreases an order of magnitude when the barrier width is increased

191

SCANNING TUNNELING MICROSCOPY

by only 1 8,. Because the current is so sensitive to barrier width, a resolution of 0.01 8, (i.e., less than 2% variation in tunnel current) normal to the sample surface can be obtained with present STMs. THE LATERAL RESOLUTION.If the same results are applied to an STM with a W( 11 1) monoatomic tip opposite to a flat sample surface, approximately 70% of the tunnel current flows through the atom on the apex of the tip, explaining the good lateral resolution of the tip. Louis et al. ( 1 988) give a more quantitative derivation by expressing the lateral resolution in terms of an effective length Leff,defined by n(Leff/2)2= l/Jz,,,=,; J,,,,, is the rnaximum current density between tip and sample. Assuming a parabolic tip with radius of curvature R, and a flat sample with a parabolic protrusion of height h and radius of curvature R,, leads to Leff = 2C(Reff/K,)H(k P)11’2.

(16)

+

Ref‘ is an effective radius of curvature, defined by l/Reff = (1/R) ( l/Rs). The function H , with the protrusion height h and the ratio between the two radii of curvature p = R/R, as arguments, is defined by H(h,B)= 1 + BexpC-2k-,h(l

+ P)/B1.

(17)

In the case of a flat sample, B 3 0, the effective length becomes Leff = ~ ( R / K , ) ” ~ ,

(18)

which leads to a lateral resolution better than 10 8, for a monoatomic tip. THE RATIO BETWEEN MEASURED HEIGHTAND REALPROTRUSION HEIGHT h. This quantity is called the sensitivity S of the STM. For the above situation, Louis et al. (1988) find

s = (1/2Koh)ln{CexP(2Koh)/(1 + B)IH(k B)}.

(19)

In Fig. 14, this sensitivity is sketched for several parameters. The absolute barrier width s plays a role in neither the lateral resolution nor the sensitivity. This is an oversimplification, since. the model takes into account only currents in the z direction. Allowing for an inhomogeneous current density inside the barrier due to the curvature of tip and sample, the above equations remain valid if Reff is replaced by Reff s.

+

B. Extended Tunnel Theory

In general, the barrier between an STM tip and sample will not be a square barrier. Because of differences in work function between both electrodes and

192

L. L. SOETHOUT et al.

-

FIG.14. (a) Sensitivity (ratio of observed to real corrugation) as a function of the ratio between tip and sample radius, for a corrugation of 1.5 and a work function of 4 eV. (b) Sensitivity as a function of the corrugation, for R / R , = 3 and a work function of 4 eV. [After Louis et al. (1988).]

the applied voltage, the barrier becomes asymmetric. Also, the classical image potential, or more generally, t h i exchange-correlation potential, should be incorporated. Therefore, a Wentzel- Kramers- Brillouin (WKB) approximation for calculation of the transmission coefficient is generally used. For the planar junction this was done by Simmons (1963), who found a significant lowering of the barrier at distances below 5 A. But even with these changes, it will be clear that a planar junction model for the STM can only be valid if the curvature of tip and sample are large compared to their mutual distance. Then the distance s in the current density of Eq. (14) may be replaced by Az(R), the local distance between tip and sample at lateral position R. In all other cases a full three-dimensional description of the tunnel process will be needed to make quantitative comparison with experimental work. The tunnel current is closely related not only to the shape of the barrier, but also to the electronic structure of the electrodes (which in turn affects the barrier). To explain the spectroscopic capability of STM, a free-electron model of the electrodes is not sufficient and local band-structure properties have to be included. The theories for calculating the tunnel current in an STM configuration can generally be divided into two classes: 1. tunneling in terms of the transmission and reflection at the barrier of incoming electron wave functions, as in Section 1V.A; and 2. tunneling in the transfer-Hamiltonian formalism, considering transitions between states of the left and right electrode.

SCANNING TUNNELING MICROSCOPY

193

1 . Scattering and Transmission at the Barrier The first method is an extension of the theory of the rectangular barrier to three dimensions and more general barriers. The electrodes remain freeelectron-like, but the incoming wave function is allowed to have a wave-vector component parallel to the junction surface as well, i.e., k, = ( K , k l z ) . For metals this approach may be justified by noting that most metals have s-like wave functions in the energy range around the Fermi level. In most tunnel theories, K is assumed to be conserved. Several groups (Bono and Good, 1985, 1986) keep essentially the plane electrode approach, but allow for more realistic barriers V ( z ) ,including effects of the classical image potential and the electrostatic potentials, that are caused by differences in work function of both electrodes and by the applied voltage difference between the electrodes. A common approach to handling such barriers is via the already-mentioned WKB approximation. This leads to a transmission probability of T ( E , K ) = exp{ - ( 8 m / h 2 ) 1 / 2 s ~ 1 2 d z [ V( z()E - ( h 2 K 2 / 2 m ) , l ) . (20)

This T ( E , K ) is equivalent to the transmission probability of Eq. (12). In general, only incoming waves with K FZ 0 will have a large transmission probability, because of the exponential decrease of T ( E ,K ) with increasing K . The current density is found by summing over all initial states k, taking into account the occupation probability of the initial and final states:

Evaluating j l z into (eh/m)k,,lAi12,converting the sum into an integral and noting that d E = dE, = ( h 2 / m ) d k , , k , , ,this leads to J, = ( e / 4 n 3 h ) s : d E [ f ( E ) - f ( E

+ eV)]

s

d2KT(E,K)

(22)

(see Duke, 1969). In the case of zero temperature, the probability function f limits the integral over E to the range between E , - el/ and E,. Finally, multiplying J, with an effective tunnel area leads to an expression for the tunnel current. Bono and Good (1985) calculated numerically the multiple-image potential for a planar junction with a hemispherical protrusion on one of the metal electrodes. By following the above derivation, calculating the current density at the apex of the protrusion, they estimated the total current from the protrusion to be of the correct order of magnitude compared with experiments. In a later paper (Bono and Good, 1986) they applied the same theory to

’

194

L. L. SOETHOUT et al.

a semiconductor sample with two parabolic valence bands, for light and heavy holes respectively. The multiple-image potential was then affected by the dielectric properties of the semiconductor. Neglecting band-bending effects, they showed that the bias voltage needs to exceed a certain threshold before a tunnel current will flow, depending on the energy gap of the semiconductor. Another approach to obtain an STM-like geometry, starting from the planar junction, has been developed by Garcia et al. (1983) and Stoll et al. (1984). The periodicity of the sample surface, due to the underlying crystal lattice, is introduced by a topographic corrugation of the sample surface, z = z,(R), where R represents the coordinates parallel to the surface. The tip is replaced by a periodic array of tips commensurate with the sample lattice, z = z2(R).The tips need to be separated sufficiently to have negligible current overlap. The tip periodicity is characterized by a surface reciprocal lattice { G } . The tunnel barrier, distorted by the image potential and the electrostatic potential, is approximated by a rectangular barrier. For an incident plane wave with wave vector k , = (K, k1J, Eq. (9) is now generalized to

+ C) - R + klZGz]}; K ~ Z+ ) ad exp(~~z)]exp[i(K + G ) R];

11/1

= AiexpC(K R - k,,z)l

11/3

=

1 G

[ ~ lexp( z -

+

G

A,,exp(i[(K

where the reflected and transmitted waves are now replaced by an infinite set of waves, due to the periodicity of the sample and tip surfaces. The position vector is expressed as (R, z). Energy conservation leads now to the following conditions:

+ k f z = (K + C)’ + kIzc = 2m/h2E; -(K + G)2 + ~f = 2m/h2(U - E ) ; (K + C)2 + kizG = 2m/h2E,. K’

(24)

The coefficients can be calculated in principle from the matching conditions on the corrugated barrier boundaries z = zj(R), j = 1,2. Actual calculations were done with only a limited number of reciprocal lattice vectors (see Stoll et al., 1984). Assuming only tunneling at the Fermi level (i.e., low bias V ) ,the total current density in region i can be calculated by Jiz

=2

1’

jizK,

K

(251

where jiiK= -(eh/rn)Im(ll/l(a~~/az)).The prime indicates summing over K, such that k, is at the Fermi surface and kl, > 0. The distribution of Jiz around the tip, the tip being at several positions with respect to the sample

195

SCANNING TUNNELING MICROSCOPY

ri

I

-1 0

-5

I

I

0

5

11

-I -

-5

R

(a)

FIG. 15. Calculated lines of constant J,,/J,, and J J J , , for a hrentzian tip aligned with a bulge of a sinusoidally corrugated sample. The Fermi energy is 1.39 eV on both sides, and the work function is 2.41 eV. The current density decreases quickly in both cases as a function of distance to the tip center, indicating a lateral resolution of less than 10 A in this case. [From Stoll, E., Baratoff, A,, Selloni, A,, and Carnevali, I?, (1984).J . Phys. C. 17,30731

corrugation, leads to a qualitative estimate of the lateral resolution of the STM (see Fig. 15). Garcia et al. (1983)found values for Leffbetween 4 and 8 A, varying linearly with the effective radius of curvature, Reff, and independent of s. This is not in agreement with the results of Louis et al. (1988), i.e., Eq. (18), or with those of Tersoff and Hamann (1985) (see Section IV.B.2). Integrating 522over a surface inside the second electrode parallel to the barrier leads to the total tunnel current

A is the total barrier cross-section and T ( E , K ) = EJA,c/Ai12k2,c/kl, is the transmission probability, in analogy with Eq. (12). The prime limits the summation to those C for which kzzc is real. Now the exponential dependence of the tunnel current on the distance between tip (plane) and sample can be examined. Stoll et al. (1 984) found that for two-dimensional tunneling the s ) occur at distances smaller than 6 A. These deviations from exp( - 2 ~ ~only deviations are mainly due to the summation over K. Garcia et ul. (1983) found that in three dimensions the current can be approximated by 1 ( s ) = (eh/2m)~~/p,(E,)G(Reff)exp( -2~eff~).

(27)

The exponential behavior can be described by Kerf, defined by ~ ~+ y(), y1 being a small correction factor (0.07 according to Garcia et af. (1983), 0.04

196

L. L. SOETHOUT et a!.

when the data from Stoll et al. (1984)are fitted to the same equation) due to the integration over K. p,(E,) is the density of states of the tip at the Fermi level, and G(R,,,) is a geometrical factor depending only on the effective radius of curvature of sample and tip. Once the differencein tunnel current is known between the situation where the tip is above a surface maximum and the situation where the tip is above a minimum, the sensitivity S , describing the corrugation of the equicurrent lines with respect to the real sample corrugation h, can be evaluated, leading to the simple expression

S

= exp[-n*(R,

+ s)/(lcoa2)],

(28) provided that the tip radius R, is large with respect to 1/lc0(Stoll et al., 1984).a represents the period of the real corrugation of the sample. This result is also obtained by Tersoff and Hamann (1985) and Louis et al. (1988). Recently a new theory based on scattering at a barrier was published by Lucas et al. (1988).Here the starting point is again the planar junction between two free-electron metals, the Hamiltonian of which is supposed to be exactly soluble. A local perturbation of the potential is introduced in a small region of space, causing most of the tunnel current to flow at the perturbation. Formally, this modified tunnel process can be handled by solving the Dyson equation for the full barrier Greens function. For practical purposes the problem is discretized by laying a grid of points over the barrier. Lucas et al. (1988) considered a hemispherical protrusion added to one of the electrodes, the tip. The image potential was also taken into account. At zero temperature and for small bias voltage, the m = 0 cylindrical wave functions turn out to carry 90% of the total current. The current density is strongly peaked at the protrusion, explaining the high lateral resolution of STM. This is in agreement with other tunnel theories. Lucas et al. (1988) also indicate the possibility of extending their theory in order to treat more realistic situations, incorporating atomic and electronic structure of tip and sample. This, however, will take more computational effort, since in addition to the more difficult wave functions, the three-dimensional barrier will also be complicated. 2. Transfer Hamiltonian Approach Because of the assumed free-electron character of the electrodes, the previous method of calculating the tunnel current cannot be applied to electrodes with a clearly pronounced band structure or with strongly localized surface states. A second approach, the transfer Hamiltonian theory, is more appropriate to handle these situations. In the framework of this theory, the tunnel process consists of a transition of an electron from a state of one electrode to a state of the other electrode. These states are considered to be

SCANNING TUNNELING MICROSCOPY

197

unperturbed, if a weak coupling is assumed between both electrodes. This approximation is questionable, since a barrier width of less than 10 A already affects the tunnel barrier appreciably. The method was first discussed by Bardeen (1961). The eigenfunctions &,, and 42nof the left and the right electrode, respectively, are no longer eigenfunctions of the total Hamiltonian of the combined electrode system. This leads to transitions between both types of states, which can be described by transition matrix elements Mnm. In the case of a free-electron Hamiltonian, Mnmcan be written as

where

LmW = (ieh/2m)CCh:n(r)V~,m(r)- 41m(r)V4Mr)l

(30)

is the current density. The surface S lies inside the barrier. The total current through the barrier, due to all possible electron states, is given by Fermi’s golden rule,

where f represents the Fermi distribution function. The Fermi energy E , is chosen to be the same for both electrodes. It can be shown that Eq. (31) is equivalent to Eq. (22) when applied to a tunnel junction with free-electron electrodes and the transmission probability given by the WKB approximation. In the case of low temperature and small bias voltage, Eq. (31) reduces to

So, in lowest order, current and voltage are linearly related, the tunnel contact being ohmic. The details of the tunnel process are contained within )MnmI2, which can be calculated via Eqs. (29) and (30). Tersoff and Hamann (1983,1985) calculated M,,, by expanding the surface wave function of the sample (right electrode) to

1c

= #~~,,(r)

ct;

exp(K,z) exp[i(K

+ C) . R]

(33)

inside the barrier (cf. in Eq. (23)).The tip is modeled as a spherical potential well with radius R and center at position ro. This leads to the following asymptotic tip wave function inside the barrier: - ro/)-’exp(-KOlr - rol). 41m(r)= ct-KOReXp(KOR)(KOIr

(34)

198

L. L. SOETHOUT et al.

Evaluating the matrix element leads to M,,, a q52n(r0), yielding finally for the current 1/1/ = (32713e2/h)q52RZK,4p,(EF)ps(T,, E F ) .

(35)

Here ps(r, E ) is the local density of states (LDOS) of the sample (electrode 2) evaluated in the center of curvature of the tip ro and at the Fermi level:

and p , ( E ) represents the density of states (DOS) of the tip. Equation (35) can be related to Eq. (15) by noting that 1d2,,(r)I2K exp( - 2 ~ ~ s )In. this way STM images can be related to properties of the sample alone: The tip follows contours of constant charge density per unit energy around the Fermi level, with the STM in the constant-current mode. Calculating STM images becomes very similar to calculating charge densities. Tersoff and Hamann also made estimations on the lateral resolution and the sensitivity of the STM. For the lateral resolution they found the same expression as Eq. (16) of Louis et al. (1988),except the factor 2 was replaced by 1.66. The sensitivity turned out to be equal to Eq. (28), found by Stoll et al. (1984). Considering a more realistic tip wave function, taking into account the real tip shape and its electronic configuration, leads to more difficult expressions for the tunnel current. For tip wave functions with an angular dependence ( I # 0), the above theory may still be used, if rn = 0 and 1 is not too large. Calculations of Chung et al. (1987) show that at least the p-wave function has to be taken into account. The s-wave tip model certainly breaks down when the curvature of the tip becomes large with respect to the barrier width, resulting in tip wave functions with large 1 (Tersoff and Hamann, 1983,1985). Feuchtwang et al. (1983) and Feuchtwang and Cutler (1987) derived a more general expression for the tunnel current in the transfer-Hamiltonian formalism, in terms of the spectral densities of sample and tip p(r, r‘, E ) = q5,$ml(r)q5n(m)(r’) 6(En,,, - E ) . This means that the tunnel current is no longer proportional to the LDOS. However, it is possible to calculate the LDOS from the measured STM image, although it might be tedious. When the STM is in the current-imaging mode, the two-dimensional Fourier transform of the tunnel current is directly related to the Fourier transform of the spectral density. From the last, the spectral density itself, and finally the LDOS, can be obtained by the reversed transformation. Fortunately, the simple expression obtained by Tersoff and Hamann does not loose all of its value, according to theoretical work of Lang (1985,1986b). By modification of Bardeen’s approach to the transfer-Hamiltonian formalism, he obtained an expression for the current density inside the tunnel barrier

SCANNING TUNNELING MICROSCOPY

199

instead of the total current. He applied his theory to the case of two planar electrodes with a free-electron character, with a realistic atom placed on one of the electrodes (the tip). Calculation of the tunnel current and its distribution inside the barrier showed an essentially cylinder-symmetric current distribution, only little influenced by rn # 0 states of the tip (Lang, 1985). If another atom is put on the sample surface, the path of the tip closely follows contours of constant LDOS at the Fermi surface, when the STM is in the constant-current mode of operation, regardless of the chemical behavior of the adsorbed atoms (Lang, 1986b). The height of the protrusion, however, as seen by STM, does depend on the electronic configuration of the adsorbed atoms, showing spectroscopic information entering an STM image (see also Lang, 1986b, 1987a).This may even result in a virtual depression of the sample surface (see Fig. 16). Lang's theory can also be applied to the original model of Tersoff and Hamann, as was shown by Leavens and Aers (1988). Relatively simple expressions for the current density and the total current are obtained in this way. Like Lang, Chen (1988) also derived a tunnel theory from an atomic point of view. He starts with a modified transfer-Hamiltonian theory, applicable also in the high bias case. The choice of Hamiltonian of the sample and the

4

3

u 2

z I v1

a

1

-1

'

-20

I

1

I

-10

0

10

20

Y (BOHR) FIG. 16. Change in tip-sample distance A s = s ( Y ) - s(w)versus lateral separation Y , when the STM is in the constant-current mode. s ( s ) is taken to be 16 bohr (1 bohr x 0.53 A). The tip atom is Na; the sample adatoms are respectively Na, S and He. [After Lang (1986b3.1

200

L. L. SOETHOUT ef

a!.

Tip State

FIG. 17. Current images calculated from the derivative rule for several tip and sample states. Tip and sample states are aligned in the center of each image. The distance between tip and sample is approximately 10 A, and the work function is 4 eV. The size of the images is about 3 A. [After Chen (1988).]

corresponding wave functions (Pznis such that the potential energy, due to the bias V, is included. By expanding tip and sample wave functions in terms of spherical harmonics (s-,p-, d-states) or parabolic (0-, 71-, 6-) states, the matrix element M,,, can be expressed in terms of a derivative of the sample wave function at the position of the tip atom. Once the matrix element is calculated, the tunnel current can be calculated. Figure 17 shows some current images obtained in this way. Sample and tip states apparently influence the tunnel signal in an equivalent way: Interchange of tip and sample state gives the same image. Another observation is that when sample and tip state have the same symmetry and orientation, the resulting current image has only a single maximum. The magnitude of this maximum can be comparable to the signal in the case where an s-wave tip scans across an s-wave sample state. This indicates that tunneling from m # 0 tip states cannot always be neglected, as assumed by Tersoff and Hamann (1983, 1985) and Lang (1985,1986b).

SCANNING TUNNELING MICROSCOPY

20 1

C . Spectroscopy In the previous section a close connection between topography, as observed with STM, and the electronic structure of the sample was derived. This suggests that STM can be used to obtain spectroscopic information on the surface, in analogy with solid-state junctions. When the bias V is increased, more electronic states can contribute to the tunnel process. In this way I ( V ) will contain information about all states in the energy window between E , eV and E , . In the transfer-Hamiltonian formalism, applied to the case of a planar junction and including many-body interactions, a general form for the tunnel current can be derived, showing the influence of the density of states:

S:i>

I ( V ) = (4ne/h) -

f(E +

d E I M ( E , V ) 1 2 [ f ( E- EF) -

EF)lpt(E)ps(E

+ ev)

(37)

(Duke, 1969). M ( E , V ) is the matrix element, describing the tunnel transition between tip states with energy E and sample states with energy E + eV. In the case of an STM geometry, the situation will be more complicated, because of the three-dimensional character of the junction and the localization of the surface states. In spite of this, Selloni et al. (1985) simply started by applying the Tersoff and Hamann result to the situation of a finite bias voltage V :

1

EF

I ( V )a

p,(E)&(ro, E

E F - eV

+ eV).

(38)

Applying a finite bias V will cause a change in the tunnel barrier with respect to the zero-bias case. Since the LDOS of the sample is evaluated at the position of the tip, it will be affected by a change in tunnel probability, as is indicated by the tilde in jjs(ro, E + e V ) . This effect can be described approximately by a bias-dependent transmission coefficient T (V ) ,which is unity for zero bias and decreases with V. Any k dependence of T is neglected. For small bias voltages, compared to the work function, T ( V ) can be assumed to be constant. Otherwise T ( V )may be calculated in a WKB approximation. By assuming a structureless DOS of the tip, Eq. (38) can be differentiated with respect to V, resulting in dl/dV a T (V)p,p,(r,, E ,

+ eV).

(39)

This means that the differential conductance, determined at a bias V, is directly related to the LDOS of the sample at energy E , + el/.

ENERGY RELATIVE TO FERMl LEVEL (eV) FOR Na

2.0

1.5

1.0

0.5

0.0

-0.5 -1.0 -1.5 -2.0

ENERGY RELATIVE TO FERMl LEVEL (eV) FOR Ca

BIAS (eV)

FIG. 18. (Top) Curves of the difference in the DOS between the metal-adatom system and the bare metal (with rs = 2) for adsorbed Ca and Na. The energy scale of Na (top) is reversed for comparison with the bottom figure.Only the states contributing significantly to the tunnel current (i.e., states with m = 0) are shown. The 3s resonance of Na lies well above the Fermi level, indicating that the 3s electron is donated to the metal. Also, in the case of Ca, the normally filled 4s state has lost some charge to the metal (low-energy peak). The 3d resonance of Ca is empty. (Bottom) The solid line is the calculated curve of ( d l / d V ) / ( l / V versus ) V for the Ca-Na tunnel system. The dashed line results from a simple model based on Eq. (39). [After Lang (1986a).]

SCANNING TUNNELING MICROSCOPY

203

Chen ( I 988) found a similar relation, starting from Eq. (37)and treating the bias distortion as a perturbation:

where c$s is the work function of the sample. When the STM is in the constant-current mode, a change in bias will also influence ro in Eq. (39), or equivalently s in Eq. (40). This will alter both the LDOS of the sample and the transmission coefficient. Experimentally, Stroscio er al. (1986) found that therefore (dZ/dV)/(I/V)or, equivalently, d(1n I)/d(ln V ) gives a better characterization of the LDOS, being relatively independent of the distance between tip and sample. The close correspondence between the LDOS and d(ln I)/d(ln V ) was illustrated by calculations of Lang (1986a). He calculated the density of states of a Na atom, attached to a flat free-electron electrode, as a function of energy. A similar calculation was performed for Na replaced by Ca. Combining both electrodes to a tunnel junction, the tunnel current was calculated in the transfer-Hamiltonian formalism, for different values of bias, keeping the barrier width constant. The resulting plot of d(ln f)/d(ln V ) versus V shows the same features as occurred originally in both LDOS plots (see Fig. 18).

V. APPLICATIONS

The results of experiments performed with STM up to 1988 are reviewed in the following sections. The surfaces are divided into the following classes: metals, semiconductors, layered materials, superconductors, insulators and magnetic materials. The outermost layer determines the category, unless it is only a few atomic layers thick and the surface properties are likely to be determined by the substrate. In the last sections special topics are considered, such as imaging of adsorbed molecules, the use of STM as a surface-modifying tool and the observation of dynamical processes. Tunnel voltages will be expressed in terms of the potential of the sample with respect to the tip. A positive bias thus means tunneling from the filled states of the tip into the empty states of the sample.

204

L. L. SOETHOUT et al.

A. Metals

Metals were the first materials to be studied by STM. Tunneling can take place at relatively low voltages (a few millivolts) because there are states at the Fermi level into or from which the electrons are able to tunnel. Since the conductivity is good, the total voltage drop occurs over the tunnel barrier and can be used directly as the energy parameter for spectroscopy. Also from the point of view of data interpretation, metals are easy to deal with. In general the wave functions of metals at the Fermi level have an s-like behavior, providing that the charge density closely follows the atomic corrugation. Therefore the images can be directly related to the surface topography. The lack of specific surface states leads in general to a smooth charge corrugation, which in turn leads to a structureless appearance of unreconstructed metal surfaces with corrugation amplitudes < 0.01 A, apart from a few exceptions. Only atomic steps and reconstructed surfaces show up clearly in tunneling microscopy. After this short introduction, we continue with a review of the experiments on specific metals, starting with the most studied ones. Compounds and surfaces of technological interest are treated last. 1. Gold Au(ll1) was the first metal surface on which individual atoms were imaged. Hallmark et al. (1987) imaged the individual atoms on a 2500-A thick film, evaporated on mica at a temperature of 300°C. These films give large terraces in the (1 11) direction, separated by monoatomic steps (2.4 A) (see also Salmeron et al., 1987; Emch et al., 1989).The minimal distance between two maximums is close to the theoretical interatomic distance (2.9 8)(see Fig. 19). The treatment of the surface does not appear to be critical. Both on unclean surfaces that had been exposed to air for months (see also Green et al., 1988b), and on UHV-cleaned surfaces, the individual atoms were imaged. The step structure of Au(ll1) faces was also investigated. Kaiser and Jaklevic (1987) found monoatomic steps parallel to [2TT] with hardly any kinks. These steps are sometimes ordered in a regular array, yielding terrace widths of 23 & 2 atomic rows (66 6 A) (see Fig. 20), which they attribute to a (23 x $3) surface reconstruction. Monoatomic steps with closer spacing were found by Brodde et al. (1988)and Emch et al. (1989).Salmeron et al. (1987)also observed monoatomic steps on a Au(433) (i.e. 7(111) x (100)) surface, the average slope of the surface being determined by the terrace width. Ocal et al. (1 988),who investigated the (755) or 6(111) x (100)face, observed the opposite effect: a constant terrace width of eight atoms and a variable step height. Spectroscopic measurements on Au(ll1) were performed by Kaiser and Jaklevic (1986) and by Brodde et al. (1988).The first authors found a peak in

SCANNING TUNNELING MICROSCOPY

205

FIG.19. Grey-scale representation of a 12 x 14 A’ region of a clean Au(ll1) thin film on mica. The atomic spacing is 3.0 & 0.3 8; the corrugation is 0.3 A. [After Hallmark et a/. (1987).J

dI/dV at 0.4 eV below the Fermi level, also observed in UPS, and an unidentified broad resonance at 0.7 eV above the Fermi level. These structures were not observed by the second group, who only observed deviations from a linear I-V characteristic at large bias (I V1 > 3 V), because of a change in the transmission probability of the barrier. On other low-index planes of Au, no individual atoms have been observed, although it is possible to image surface reconstructions. Binnig et al. (1983b) found Au(ll0) to consist of channels in the [IT01 direction with lengths of several hundred angstroms. The channels could be interpreted as (1 x 2), ( 1 x 3) and sometimes (1 x 4) reconstructions, depending on the width of the channels (see Fig. 21). The (1 x 2) reconstruction could be explained by a missing-row model, whereas the ( 1 x 3) reconstruction leads

FIG.20. Part of a clean Au( 111) surface, 550 x 1400 A*, showing an array of monoatomic steps aligned with the [2TT] direction. The distance between two steps is 66 6 A (i.e., 23 2 atomic row spacings). [After Kaiser and Jaklevic (1987).]

+

FIG.21. Part of a Au( 110)surface containing several reconstructions and also some disorder. The tick marks on the crystal axes indicate 5 A. The straight lines represent the terraced structure with monoatomic steps (e.g., at S); below each line the missing rows and above each line the remaining rows are enhanced. The numbers on the top scan give distances between maxima in units of the atomic-row distance. The inset shows the structural model for the part between A and B. [After Binnig er al. (1983b3.1

207

SCANNING TUNNELING MICROSCOPY l

r

'

.

.

,

,

'

,

'

,

'

~

'

'

,

' 40"

'

GAP BIAS VOLTAGE FIG.22. Experimental curves of d l / d V (closed circles) versus bias for Au(1 lo), showing the Gundlach oscillations. The oscillatory solid curve is the theoretical barrier penetration factor. The dashed curve omits the image-potential contribution. The experimentally determined barrier width is also indicated. [After Becker cr a/.,(1985a).]

to facets of three atomic rows. The (1 x 4) reconstruction is a combination of both effects. Garcia et al. (1983) and Tersoff and Hamann (1985) used the (1 x 2) reconstruction to test their theoretical models. The only spectroscopy on Au( 110) was concerned with image states (see Section ILC), observed for the first time by Binnig and Rohrer (1982). Also, Becker et al. (1985a) observed these Gundlach oscillations and were able to fit them with theory (see Fig. 22). Calculations of Garcia et al. (1987) are in good agreement with their findings. Au( 100)was investigated by Binnig et al. (1984c),who found large terraces, separated by monoatomic steps. A ( I x 5) reconstruction appears as long channels parallel to [Oll] on top of the terraces (see Fig. 23). A closer look reveals slight periodic differences in the structure of the (1 x 5 ) cells, leading to a larger "unit cell" of approximately 130 x 70 A'. The proposed model for this structure is the presence of a hexagonal ("close-packed") overlayer, incommensurate with the underlying lattice. Kaiser and Jaklevic (1 986) performed spectroscopic measurements on the (100) surface, but found no evidence for surface states.

FIG.23. Part of a clean (1 x 5 ) reconstructedAu(100) surface with monoatomic steps. The tick marks on the crystal axes indicate 5 A.The inset shows the LEED pattern of the predominant (1 x 5 ) corrugation. [After Binnig et al. (1984c).]

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209

Besides the crystalline surfaces of Au, the surface of evaporated and electrochemically deposited Au also has been imaged. Drake et al. (1986) imaged Au plated on highly oriented pyrolitic graphite (HOPG), the surface consisting of rolling hills approximately 100 A wide. Similar features occurred when a 1000-A thick Au film was deposited on glass (Schneir et al., 1988a). Besenbacher et al. (1988) and Warmack et al. (1988) evaporated a Au film on Si(11I), resulting in the formation of islands (100-300 A in diameter, 30-100 A in height). Both observations are in contrast to the findings of Jaklevic e f al. (1988a) and Pappas et al. (1988),who found that an evaporated Au film follows the structure of the underlying surface closely without any islands or monoatomic Au steps present. Spectroscopy on polycrystalline uncleaned Au was performed by Jahanmir et al. (1988) in air, using the CITS technique. They obtained very nonlinear I - V characteristics, which they interpreted in terms of Schottky emission (i.e., el/>>q5 and eV >> kT), where I cc exp(AV”*) for large V. This leads to low barrier heights on the order of 0.3 eV and large barrier widths of 200-1000 A. Large barrier widths were also observed on a Au film on Si, where the contact point between tip and sample occurred only after a tip displacement of 300 A. Similar I - V characteristics were obtained by West et al. (1986) and Ramos et al. (1988). 2. Nickel The ( 1 11) face was studied by van de Walle et al. (1987a) on a stepped Ni(7 9 I 1) (i.e. 5( 1 1 1) x (170))surface. The (1 1 1) surface consists of a p(2 x 2) reconstruction, probably induced by adsorbed H (two atoms per unit cell) (see Fig. 24). The corrugation is also observed in measurements of dI/dV over the surface. The reconstruction is also seen on the multiatomic steps. The step terraces are protruded at the upper step edge and indented at the lower edge. This might be due to a charge transfer in the stepped regions, responsible in general for a decrease of the work function at high-index faces. Calculations of Doyen and Drakova (1986) show this effect for a step on Ni(100). Local spectroscopic measurements reflect some structure of the Ni DOS, a Hinduced peak and sometimes a double-peak structure around 250 mV below the Fermi level-tentatively attributed to the stretch mode of adsorbed CO, and therefore an inelastic contribution! The Ni(ll0) surface is only imaged with adsorbates. Baro el al. (1984) found an 0-induced (2 x 1) reconstruction, providing evidence for a sawtooth structural model. Also, domain walls were observed where a shift in reconstruction occurs. Kuk et al. (1987a) imaged the Ni( 110)+ H surface, which gives in LEED measurements a “streaky” (1 x 2) pattern. Besides large regions of disorder and incidental regions of (1 x 2) and (2 x 1)

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FIG. 24. Topographic grey-scale image of a stepped Ni(l11) surface presumably covered with a monolayer of H. A p ( 2 x 2) reconstruction is observed, extending over the step. The H atoms are situated on the corners of the hexagons. [After van de Walle et al. (1987a).]

reconstructions, the main reconstruction is ( 5 x 2), caused by a combination of row pairing parallel to [lTO] and missing rows parallel to [OOl] (see Fig. 25). Along the missing rows the work function increased by 0.3-0.4 eV. The reconstruction is formed by a transport of Ni over the surface, in contrast to the former 0-induced reconstruction, where the 0 itself is imaged. Defects and domains were also seen for this reconstruction. On a Ni( 110)-Au(0.8% at.) with 0.9 monolayers of Au segregated from the bulk

FIG.25. 120 x 90

Ku k et al. (1987a).]

A2 topographic image of

the Ni(110)(5 x 2)-H reconstruction. [After

21 1

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to the surface, Kuk et al. (1987b) observed a (7 x 4) reconstruction, leading to chains of Au atoms parallel to [OOl]. A c(2 x 4) subunit can be distinguished, which also shows up in LEED patterns. Sometimes connections between adjacent Au chains are observed in the form of Au bridges. Other reconstructions are also observed, mainly at lower coverages. On Ni( 100)only spectroscopic measurements were performed. Binnig et al. (1985a)investigated image and field states on Ni(100), Ni(100)c(2 x 2)-0 and on dirty oxidized Ni. Because of a 7.1-eV wide band gap in the projected DOS for this surface, sharp states were observed inside the gap, in good agreement with simple theory. Spectroscopy at lower energy on Ni( 100) covered with three monolayers of oxygen led to three peaks in dZ/dV between 0.6 and 1.7 eV above the Fermi level and a broad peak at 5.5 eV. The three peaks are due to tunneling into conducting oxide states (Garcia et al., 1986).

3. Silver The only experiments on single-crystal surfaces of Ag were performed by Benistant et al. (1986), who compared the structure of etched Ag(100) and Ag(ll0) surfaces. The (100) surface consists mainly of large flat terraces, separated by steps, while the (110) surface shows a more hilly character (see Fig. 26). These observations were shown to be in agreement with experiments using transverse electron focusing (TEF). STM on Ag films is mainly concerned with the relation between the preparation of the film and its topography. The roughness of the surface is especially interesting, since this plays a dominant role in surface-enhanced optical phenomena, such as Raman scattering. Such effects were also observed in STM on Ag by Coombs et al. (1988), who investigated inverse photoemission by using tunneling electrons as incoming particles (see Section V1.A). The temperature of the substrate during deposition of the film determines to a great extent the quality of the film. Deposition at room temperature leads to large crystallites (500-1000 A diameter) with smooth boundaries (Raether, 1984; Gimzewski et al., 1985). Films deposited at 100 K, however, show

(4

(b)

FIG.26. (a) An Ag(100) surface of 1450 x 1300 A*, showing atomically flat regions, separated by a large step of about 50 A. (b) An Ag(l10) surface of the same dimensions as the previous one, showing a smoothly varying structure. [After Benistant et a/. (1986).]

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smaller structures (100-200 A diameter) separated by deep trenches, especially when pyridine is adsorbed before annealing to room temperature (Gimzewski et al., 1985;Humbert et al., 1985).The surface condition of the substrate is also of importance. Warmack et al. (1988) evaporated a thin Ag film on Si under UHV conditions, leading to flat plateaus of Ag(l1 l), aligned along the substrate crystallographic axes and separated by monoatomic steps of Ag or Si. In contrast, films of Ag evaporated on Si(ll1) and annealed at 200°C in air show spherical-shaped islands with a size of 250-300 A. The Ag surface can also be prepared in an electrochemical cell, by etching or plating. The STM should then be operated with the sample submerged in the solution. Aktsipetrov et al. (1988) observed an increase in roughness when a few atomic layers were etched, resulting locally in structures 10 A in height and 15-20 A in length. Sonnenfeld and Schardt (1986) and Itaya and Tomita (1988) plated a flat surface of HOPG with Ag, which results in smooth hills, similar to the crystallites on evaporated Ag (see Fig. 27). This process is reversible.

FIG.27. An HOPG surface of 900 x 1500 A’, plated with 3.9 mC/mm2 Ag. The image was taken in a solution of AgCIO,. [After Sonnenfeld and Schardt (1986).]

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4. Aluminum The topography of Al(111) surfaces was investigated by Wintterlin et (11. (1989), who found large terraces 100 A in width, separated by monoatomic steps. On the terraces individual Al atoms could be imaged, with an interatomic distance of 2.86 A and a corrugation of 0.1-0.4 A, independent of the applied bias. The corrugation, much larger than expected from Hescattering experiments and theory, is probably caused by interaction forces between the tip and the sample (Soler et al., 1986; Durig et al., 1988). Wintterlin et al. (1988) observed the 0 adsorption on Al(111) to occur in islands of 10-20 A width, randomly distributed over the flat terraces. After an 0-covered surface is sputtered and annealed, other forms of oxidation are also found (see Fig. 28).

5. Platinum The clean Pt( 100)surface was studied by Behm et al. (1986) and Ritter et al. (1987). Large flat regions were found, separated by mono- and biatomic steps. On top of the flat regions, rows of atoms were observed, 0.4 A high and 14 A apart, caused by a ( 1 x 5) reconstruction formed by a hexagonal topmost

FIG. 28. Grey-scale representation of a partly oxidized Al(111) surface. The atomic structure of the A1 is clearly seen. The two hexagonal depressions with a protrusion in the middle were identified at first as oxide nuclei, but have recently been attributed to the presence of C atoms. [From Wintterlin, J . , Brune, H., Hofer, H . , and Behm, R.J., (1988). Appl. Phys. A. 47,99.]

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layer. As in the case of Au(100)(1 x 5 ) there is a slight mismatch with the underlying lattice. Under the adsorption of gas, such as CO, NO or C,H,, the reconstruction changes to a normal (1 x 1) structure (perhaps seen by Elrod et al., 1986), the excess Pt atoms forming hillocks one monolayer in height (Hosler et al., 1986). Pt films were investigated by Miranda et al. (1985), who found columnar crystallites after deposition on mica, and by Green et al. (1988a) and Schneir et al. (1988b),who found rolling hills on a glass substrate, as was also seen on Au and Ag films. Electrofaceted surfaces of polycrystalline Pt are smoother than untreated surfaces, (1 10)-oriented facets leading to flat terraces and oriented steps, and (100)-and (1 1 1)-oriented facets leading to aligned features such as grooves and wells (Gomez et al., 1986; Vazquez et al., 1987a,b). 6. Other Elements

Cu has been investigated only by Brodde et al. (1988) on (111) surfaces, revealing flat terraces separated by monoatomic steps, as well as regions of disorder. High-resolution images on the terraces reveal a x &)R30" reconstruction, probably caused by the presence of adsorbates. Spectroscopy at constant barrier width revealed no pronounced features, in contrast to other surface spectroscopies. Mo(001) covered with a monolayer of S appears to be rather inert in air and was studied by Marchon et al. (1988a,b). Topographic and, more clearly, barrier-height images reveal a p(2 x 1) reconstruction, leading to a pseudohexagonal arrangement of the S atoms on top of the Mo (see Fig. 29). The reconstruction leads to the formation of domains with different orientation. (1 x 1) areas are also observed. In a similar way, Marchon et al. (1988~) investigated Re(0001)covered with 0.5 monolayer of S in air. At a large scale, they observed flat areas separated by mono-,and multiatomic steps. Barrier-height images showed a drop in work function at step sites. Atomic-resolution ima es of both topography and barrier height on the terraces reveal a (&x 3)R30"-2S reconstruction. Pd(100) was imaged by Ringger et al. (1986), who observed both flat terraces and richly stepped areas. On Nb films, contradictory results have been obtained. Whereas Golyamina and Troyanovskii (1986) find a rather smooth surface on a film deposited at room temperature and a rough surface on a film made at 85OoC, Walsmley et al. (1988) observed the opposite. Pb was investigated at cryogenic temperature by Ramos et al. (1988), revealing a rather smooth topography. At 77 K, a straight 1 - V characteristic is obtained, whereas in the superconducting state at 4.9 K, an energy gap of 1.25 meV could be obtained by fitting the I - V curve with a BCS model.

(a

J

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FIG.29. (a) Barrier-heightimage of a 55 x 25 A’ region of Mo(001)p(2 x I)& (b) and (c)are possible models for the reconstruction. The open circles represent Mo; the black circles represent S. In view of the uniform corrugation along [1201, model (c) is favored. [After Marchon er al. (1988a).]

On polycrystalline Ta, spectroscopic measurements were performed on the image states by Coombs and Gimzewski (1988).As many as 40 oscillations in d l / d V versus V were observed, by a special trick of increasing the modulation voltage with increasing bias in order to compensate for the diminishing amplitude of the oscillations. The peak positions satisfy reasonably the relation V , a n2I3,derived from simple theory, although little deviations occur as a function of lateral tip position. The image states were also observed in inverse photoemission experiments where the incoming electrons were supplied by electron tunneling from the tip (Gimzewski er al., 1988). 7. Compounds and Alloys Several metallic glasses were studied. Ringger et al. (1986) studied splatcooled Pd,,Si,, , In air, droplet-like features were observed, whereas after gentle cleaning in UHV one could observe wavelike structures with a periodicity of 35 A and a corrugation of 3 A, attributed to a frozen surface wave. Pd60U20Si20appeared to consist of microparticles (100 A) with smaller domains on top (Bretscher et al., 1987), whereas Rh,,Zr,, showed only a little

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corrugation, due to small steps and crystallites (Wiesendanger et al., 1987). On the icosahedral Al,,Mn,,, pentagonal domains were imaged of 40-,~f dimensions (Wiesendanger et al., 1988). foil consisted of 60-A grains Some films were also investigated. A after annealing and quenching (Elrod et al., 1986).Brunner et al. (1987)imaged a 500-A thick PdzSi film on Si(lOO), on which substantial changes in work function occurred over the surface, attributed to chemical inhomogeneities due to adsorbates. 8. Surjiaces of Technological Interest

The results on such surfaces are normally very vague, in terms of the general condition of the surface (roughness, dimensions of structures). We name them briefly for completeness. Garcia et al. (1985) investigated several technological surfaces (micrometer head, injection piston) to formulate a roughness standard. Anders et al. (1988) measured the topography of a microbridge of a dc SQUID, made in a Nb film by electron-beam lithography. Vazquez et al. (1988) investigated the stamper of an optical disk, replicated by Ni electrodeposition. Both Anders et al. and Vazquez et al. find agreement with SEM images. Baro et al. (1986) found a rough topography on polycrystalline Ti used for clinical implants. Green et al. (1988a) investigated the surface of a Pt film on glass and W/C multilayers on glass, used for x-ray reflection. B. Semiconductors

Semiconductor surfaces, especially when reconstructed, often lead to beautiful STM images with clearly resolved atomic features. Unlike metals, semiconductors often possess surface states around the Fermi level, giving rise to this rich structure. There are, however, some difficulties with the imaging of semiconductors. Tunneling to or from a semiconductor can be troubled by the low conductivity of the sample. Because of the band gap of a semiconductor, the number of free carriers at room temperature is low, especially at low doping rates. Even when surface states are present in the band gap, tunneling to or from these states may be limited by the conduction process between these states and the bulk. The asymmetry caused by the vacuum interface gives rise to band bending inside the semiconductor. The amount of band bending at the vacuum interface depends on the number, the mobility and the diffusion length of the carriers. This may give rise to a Schottky barrier, too large for the electrons to tunnel through. A second effect is that all electronic levels shift by the band bending, in this way obscuring spectroscopic results. When surface states are present, the band bending is highly determined by these states, since they pin

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the Fermi level. In the absence of surface states, the band bending depends on the applied electric field between sample and tip. Another effect concerning the conduction of the electrons inside the semiconductor is caused by the special STM geometry of a sharp tip opposite to the sample. This causes the tunnel current to be injected into the sample over only a small area. Then the conductivity of the sample is determined by the so-called spreading resistance,

R , = pVA, (41) where p is the bulk resistivity of the semiconductor, and 1 and A are the effective length ( x10 A) and section ( x25 A’) of the current lines spreading near the tunnel contact (Flores and Garcia, 1984). The spreading resistance can be comparable to the tunnel resistance, resulting in a considerable voltage drop over the sample when a voltage is applied between sample and tip. This also leads to a distortion of spectroscopic data, since the applied voltage no longer represents the energy of the tunneling electrons relative to the Fermi level. Besides spectroscopy, work-function measurements are also affected, leading to smaller apparent barrier heights, since modulating the barrier width induces a modulation of the potential drop inside the semiconductor (Weimer et al., 1989).To minimize the above-mentioned effects, the conductivity of the semiconductor should be increased. This can be attained by increasing the temperature (see, for example, Binnig el al., 1983a); by using strong doping, as is usually applied; or by irradiating with light, thereby exciting valence electrons into the conduction band (van de Walle et al., 1987b). Despite the above restrictions, STM can be applied to most semiconductor surfaces without a great disturbance of the surface by dopant atoms. A great deal of work has been performed on Si and GaAs, revealing the details of many reconstructions. Some of these reconstructions, such as Si(ll1)(7 x 7), Si(111)(2 x 1) and GaAs(llO)(l x l), are well understood now, thanks to STM observations. Many other reconstructions, though imaged successfully with STM, still wait for a conclusive structural model. Also, the mechanism and the conditions of formation of most reconstructions are still unclear. Below we review the main achievements of STM in the semiconductor field. 1. Silicon

Si was the first semiconductor studied with STM. This started with the (111) surface, on which Binnig et al. (1983a) revealed the structure of the (7 x 7) reconstruction. The unit cell consists of two triangular subunits, each one containing six maxima, attributed to the dangling bonds of Si adatoms (see Fig. 3 la). At negative sample bias an asymmetry in topography between both triangles has been observed, the one pointing in the [llz] direction lying

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somewhat lower, whereas at positive bias the unit cell appears symmetric (Becker et al., 1985b; Binnig et al., 1985c; Hamers et al., 1986a; Tromp et al., 1986; Park et al., 1987; Berghaus et al., 1988a,b). This indicates that spectroscopic effects play an important role in the STM imaging of the (7 x 7) reconstruction. Binnig et al. (1983a)explained their measurements by a model in which the adatoms are placed on top of bulk silicon, thereby creating an asymmetry between both halves of the unit cell. A model that also explains the deep corner holes of the unit cell (see Tromp et al., 1986) was presented by Takayanagi et al. (1985). This so-called dimer adatom stacking-fault (DAS) structural model describes the (1 11) surface in terms of two reconstructed layers, with 12 adatoms on top. The first layer below the adatoms contains a stacking fault in the triangle pointing in the [Ti21 direction. The DAS model is reproduced in Figure 30. More support for the DAS model came from Hamers et al. (1986a, 1987a), who performed spectroscopy on the (7 x 7) reconstruction by way of the

b

FIG.30. DAS model of the Si(111)(7 x 7) surface. (a) Top view. Atoms on (1 11) layers at decreasing heights are indicated by circles of decreasing sizes. (b) Side view. Large open and solid circles indicate atoms on the (101) plane through the long diagonal across the corner holes. Smaller open and solid circles are atoms on the next (101) plane. The unfaulted half of the unit cell is on the right-hand side of the image. [After Takayanagi et al. (1985).]

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FIG.3 I. CITS difference images of filled Si(1 1 1)(7 x 7) surface states. (a)Topographic image, obtained at a bias of + 2 volt. The unit cell is indicated, the left-hand side being the unfaulted half. (b)-(d) Difference images showing, respectively, an adatom state at -0.35 eV, a dangling-bond state at -0.8 eV and a backbond state at - 1.7 eV. [After Hamers et a/.(1987a).]

CITS method, described in Section 1I.C. Current images at several positive and negative biases, with the tip position stabilized at + 2 V, reveal a rich structure. In order to obtain information on the LDOS the current images were differentiated by subtracting images of successive biases (see Fig. 31). At -0.8 V, maxima arise between the positions of the adatoms, just where the dangling bonds from the first layer are situated according to the DAS model. Binnig’s model would have given rise to an asymmetry between both halves of the unit cell. Two more states were observed: one metallic-like state around the Fermi level, centered on the adatoms, and a Si-Si backbond state at - 1.7 eV, located around the adatoms and inside the corner holes. Berghaus et al. (1988a,b) performed similar measurements, but at different tip stabilization voltages. I - V curves at several positions in the unit cell show globally the same features as described before, but differ quantitatively for + 2 V and -2 V stabilization voltages. This indicates that current imaging depends both on spectroscopy and on topography (i.e., stabilization voltage), and that AI/AVversus V is not a direct measure for the LDOS. In particular, the large current from the first-layer dangling bonds at -0.8 eV is not caused by a large LDOS, but rather by an increased transmission probability.

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Becker et al. (198%) imaged double-layer steps (3.1 A high), perpendicular to the [ 1121 and [Ti21 directions, the (7 x 7) reconstruction persisting up to the steps and the step edges coinciding with the unit-cell edges. Also, Binnig et al. (1983a) and Berghaus et al. (1988b) observed hardly any disturbance of the (7 x 7) reconstruction by defects and domain boundaries. These observations relate the occurrence of the (7 x 7) reconstruction to a very short-range interaction. The (7 x 7) reconstruction is created by slowly cooling down a clean Si(111) surface after annealing at approximately 900°C. Other reconstructions are observed when long-range ordering is prohibited. One way to attain this is by applying a fast cooling rate (> 150"C/minute) after annealing, leading to irregular areas among (2 x 1)-reconstructed areas (Pashley et al., 1988a). Laser annealing also results in a variety of reconstructions (Becker et al., 1986):(2 x 2), 4 4 x 2), x fi) R30", (5 x 5),(7 x 7) and (9 x 9). A second way is to introduce defects and steps by using vicinal(ll1) surfaces, which can x f i )R30"-reconstructed stepped area (Berghaus et al., 1987b). lead to a When the (111) surface is created by cleavage under UHV conditions instead of by annealing, a stable (2 x 1)reconstruction is formed. STM images show chains parallel to the [Oli] direction, with a lateral spacing of approximately 6.9 A, accounting for a periodicity of two unit cells (Feenstra et al., 1986).Images with a higher resolution also show the internal chain structure, with a periodicity of one unit cell (Stroscio et al., 1986,1987a).A phase shift of 180" along the chain and a small shift of the whole chain in the perpendicular direction occur upon reversal of the tunnel bias (see Fig. 32). These

(a

(8

FIG.32. Topographic STM images of Si( I 1 1)(2 x I), acquired simultaneously at biases of (a) + 1.0 and (b) - 1.0 volt. The surface heights along the [Oil] direction in the two images are out of phase. [After Stroscio el al. (1987a).]

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22 1

(b) CHAIN MODEL TOP VIEW

( C 4 0

c@ 13

rd SIDE VIEW

FIG.33. n-bonded chain model for Si( 1 I 1)(2 x I), which gives rise to zigzag chains along the [OlT] direction. The unit cell is indicated. [After Pandey (1981).]

results are consistent with the n-bonded chain model of Pandey (1981) (see Fig. 33). STM does not image the Si atoms in the chain (two per unit cell) but merely their bonding (n)state for negative bias and antibonding (n*)state for positive bias. Both states give rise to a surface band gap of 0.45 eV, which is smaller than the expected projected bulk band gap. The band gap is observed . spectra are independent in spectroscopic measurements of (dI/d V ) / ( I / V ) The of the doping concentration of the Si, indicating that the Fermi level is pinned by the surface states. Spectroscopic measurements of I versus V at several tipsample distances s can be used to determine the decay of the wave functions into the vacuum, which contains information on the parallel wave vectors K involved. For states near the band-gap edges, i.e. the n and n* states, IKI is found to be approximately 1.1 A-' . According to Tersoff (1986),this leads to a nodal structure of the wave functions, explaining the high resolution obtained on this surface. Steps on the (2 x 1) reconstructed surface have also been investigated (Feenstra and Stroscio, 1987a). The steps, with a height of one double layer, are predominantly oriented perpendicular to the [2iT] direction. The reconstruction continues up to the step edge. In the case of the step being parallel to the chains, two kinds of step structures are observed, with one and two maxima, respectively, along the [2fT] direction. The former structure is associated with a n-bonded reconstructed step. The reconstruction of Si(ll1) may also be changed by deposition of a (sub)monolayer of another material on top of it. Sometimes the (7 x 7) reconstruction remains visible, as in the case of NH, (Wolkow and Avouris, 1988a)and O2adsorption (Leibsle et al., 1988),where only the dangling bonds are saturated. In the case of submonolayer deposition of In or Ga, the Si

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adatoms are replaced by In or G a atoms (Park et al., 1988b).Epitaxial growth is reported for In at higher coverages (Nogami et al., 1987). Island growth occurs when Ag, Cu (Tosch and Neddermeyer, 1988a,b) or Pd (Kohler et al., 1988) is deposited. Nucleation starts preferentially at the faulted half by a coupling to the dangling bonds of the inner adatoms and of the first layer. At higher coverages the clusters expand until the surface is totally covered with metal islands (van Loenen et al., 1987). Adsorption at elevated substrate temperature or followed by annealing replaces the (7 x 7) reconstruction with a new reconstruction-in many cases (fix R30", which is abbreviated The group-I11 metals B (Dumas et al., 1988a) Al (Hamers and Demuth, 1988),G a (Chen et al., 1988; Nogami et al., 1988)and In (Nogami et al., 1987) give rise to a reconstruction with one maximum per unit cell, as observed in STM images. In the case of the latter three metals, the maximum is attributed to an adsorbed atom at a threefold hollow site which thereby saturates all Si dangling bonds. In the case of B, the B is substituted on Si positions in the second layer and the maxima are formed by Si adatoms. Two types of threefold hollow sites are possible: a T4 or an H 3 site, the former with and the latter without a Si atom in the second layer below. Calculations indicate that the T4 position is favored. This is experimentally verified in the case of A1 and G a by comparing the lattice registration of the 8 reconstruction with a locally present (7 x 7) reconstruction. The & reconstruction is electronically different from the (7 x 7) reconstruction. In the case of A1 a band gap is observed between -0.3 and + 1.0 V. Peaks at - 1.5 and + 1.0 V, localized at the A1 positions, are in agreement with (1)PSexperiments. A monolayer of CaF, also gives rise to a ,b reconstruction (Wolkow and Avouris, 1988b).Here the Ca is probably imaged, most F being desorbed. The precise bonding sites are not yet known. Au on Si(ll1) also results in a & reconstruction with one maximum per unit cell (Dumas et al., 1988b), tentatively explained by a trimer model. When Ag is adsorbed, two maxima per unit cell are observed in the $3 reconstruction, leading to the honeycomb structure imaged with STM. On the basis of spectroscopic measurements, van Loenen et al. (1987) modeled the unit cell to consist of a Si top layer with one vacancy, thus creating a honeycomb, and three Ag atoms forming a trimer around the vacant Si atom by filling hollow positions between the top and the next Si layer. This model was ruled out, however, by Wilson and Chiang (1987a,b), who found, by registry with (7 x 7)-reconstructed parts of the surface, that the protrusions are on hollow H3 positions and are therefore associated with the Ag atoms (see Fig. 34) Other unit cells are also observed on adsorbate-covered Si(111).In and G a cause a large variety of reconstructions besides the above-mentioned & reconstruction, depending on the coverage (Nogami et al., 1988; Park et al., 1988b): x x (4 x 1) and (1 x 1) respectively (6.3 x 6.3), (11 x 11) and ( 6 . 3 f i x 6.3&). A complicated unit cell arises upon ad-

a)

8.

(m m),(a a),

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FIG.34. STM image of a Si(l1 I ) surface showing a domain boundary between a (7 x 7) and an Ag-induced (&x &)R30" reconstructed area. The unit cells are indicated. The image has been processed in order to enhance the contrast of the (4x &)R30" area. [After Wilson and Chiang (1987b).]

(aa)

sorption of Ni, yielding a x R23.4" reconstruction (Wilson and Chiang, 1987~). Here only one Ni atom per unit cell is involved, situated in a sixfold hollow position between the first and second layer. The unit cells contains seven maxima, caused by Si adatoms. Deposition of approximately one monolayer of Cu does not result in a (1 x 1) reconstruction, but rather in irregularly spaced (5 x 5) subunits, centered near regions of favorable registration in order to relieve strains associated with the lattice mismatch between the Cu and Si lattice (Wilson et ul., 1988). A simple (1 x 1) with one maximum per unit cell does occur when As (Becker et al., 1988a) or H (Tokumoto et al., 1988) is adsorbed. In the first case the Si in the top layer is replaced by As. At positive bias, the maxima coincide with the Si positions in the second layer; at negative bias, the As is imaged, although with less resolution. The adsorption of H is thought to fill the dangling bonds of the top Si layer. Spectroscopy on such a H-terminated surface involves band bending and is sensitive to the doping level since there are no surface states to pin the Fermi level (Bell et al., 1988a).

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Other low-index planes of Si also undergo surface reconstructions. On Si(OO1) a (2 x 1) reconstruction is commonly observed with LEED. STM images obtained at negative bias show rows parallel to [liO], separated by twice the lattice constant (Tromp et al., 1985; Hamers et al., 1986b).The maxima that build up the rows are separated by a single lattice spacing parallel to the row and are often located in a zigzag pattern. The latter gives rise to a local p(2 x 2) or c(4 x 2) symmetry, depending on the phase shift of the zigzag between subsequent rows. Probing the surface with positive bias, however, leads to two maxima per (2 x l ) unit cell, tending to a (1 x l) character (see Fig. 35a and b). A model to explain above features is a dimerization

FIG.35. STM topographic images of Si(oO1)(2 x 1). In (a) the filled states (bias 1-2.0 volt) and in (b) the empty states (bias + 1.2 volt) are imaged. In (c) and (d) the occupied states of NH,dosed Si(OO1) are shown (bias -2.0 volt). In all figures the indicated unit cell contains one complete dimer. The short edge of the unit cell is parallel to [lie], the direction of the dimer rows. In (a) a missing dimer can be seen; (d) contains a monoatomic step, indicated by the line. The upper ( U ) and lower ( L ) terraces are indicated. [After Hamers et al. (1987a).]

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parallel to [I1 101, leading to rows of dimers parallel to [IiO]. The zigzag is caused by an alternation of buckling of the dimers along the row. Although the dimer bonding itself is governed by a low-energy c bond, STM images the n bond (Hamers er al., 1986ab). Spectroscopy indicates that the corresponding states give rise to a band gap of 0.35 eV and peaks at -0.8 and +0.35 eV. Imaging at negative bias probes the n bonding states in the center of the dimers, leading to rows in the topography, whereas imaging at positive bias gives maxima at the positions of the n* antibonding states, leading to the virtual (1 x 1) structure. The images of Hamers et al. (1986b) show a large number of defects, mainly missing dimers, apparently necessary to stabilize the surface. Steps also occur frequently. Diatomic steps oriented perpendicular to the dimer rows are energetically favorable and therefore frequently observed in STM images (Wierenga et al., 1987). When kinks occur in these steps, the double steps change into two single steps, since double steps parallel to the dimer rows have a high energy. The (2 x I ) reconstruction is preserved upon dissociative adsorption of NH, (Hamers et al., 1987b), leading to Si-H bonds (see Fig. 35c and d). This influences the spectroscopy, changing the 7~ bonding character. Ni impurities on Si(OO1)induce the formation of long missing-dimer channels perpendicular to the dimer rows, leading to an average (2 x 8) symmetry of the surface (Niehus et al., 1988). These channels typically have a structure consisting of a single dimer surrounded by one or two missing dimers in the [ l i O ] direction. At the position of the two missing dimers, the second-layer Si is probably absent, leading to a dimerization of the third layer, which might be the driving force for the ordering of the vacancy channels. The Si(110) surface is known to have many different reconstructions, dependent on the heat treatment of the surface. Van Loenen et al. (1988) investigated the

(i 'i)

reconstruction on clean Si(1 lo), leading to high and

low terraces differing by one monolayer. On both types of terraces zigzag chains are visible on an atomic level. This reconstruction is destroyed by a small contamination with Ni or Cu to result in a (5 x 1) reconstruction. This reconstruction is also observed by Becker et al. (1988b). At higher coverage a (2 x 5) reconstruction is formed, which was extensively studied by Neddermeyer and Tosch (1988). STM images of the latter show chains parallel to [TlO], consisting of V-shaped protrusions. Details of the protrusions can be observed at positive bias. Although the unit cells are commensurate with the bulk lattice, there is no simple model to explain the observed structures, and a distortion of more layers is probably required. Berghaus et al. (1987a,1988a) studied the high-index faces (1 12) and (223) of Si. Both surfaces can be viewed as stepped (1 1 1 ) surfaces with steps pointing in the (001)direction. STM images show that both surfaces are unstable

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in the sense that long-range ordering is absent. There is some ordering in the [I10) direction, leading to single, twofold or fivefold periodicity. The twofold periodicity can be attributed to dimerization. On the (112) faces, (1 11) terraces can be observed with a width varying between 10 and 15 A and separated by double-layer steps parallel to the [TlO] direction.

2. GaAs GaAs is another semiconductor that has been studied extensively with STM. The (110)face is very interesting since it contains both G a and As atoms. According to Feenstra and Fein (1985), the clean (110) surface exhibits a (1 x 1) periodicity with one maximum per unit cell, which has dimensions of 5.65 A along the [OOl] direction and 4.00 A along the [lTO] direction. These values agree with the bulk lattice parameters of GaAs. Since As is more electronegative than Ga, it is expected that the occupied states are situated on the As sites and the empty states on the G a sites. This explains why only one maximum per unit cell is seen, since STM images either the empty states (at positive bias) or the filled states (at negative bias). It also leads to a lateral shift of the maxima in an STM image upon reversal of the bias, as observed by Feenstra et al. (1987) and shown in Fig. 36. Precise observations of the lateral shift of the maxima indicate that the As is situated at an elevated position with respect to the G a from the same layer, because of a buckling of 2931". The DOS as determined by STS shows a band gap of 1.43 eV, almost equal to the bulk band gap, surrounded by peaks in the conduction and

+

FIG.36. Topographicimages of GaAs(l10) acquired at (a) 1.9 and (b) - 1.9 V.(c)Top view of the surface atoms. The open circles represent As atoms, the closed circles Ga atoms. The rectangle indicates a unit cell, whose position is the same in all three figures. [After Feenstra et al. (19871.1

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valence band. Inside the gap another peak is observed, attributed to a dopant state. The Fermi level is determined by the kind of doping, which indicates that no surface states are present. A detailed theoretical model can account for the spectra by taking into account a slight band bending(Feenstra and Stroscio, 1987b). For submonolayer adsorption of 0 on n-GaAs, the 0 atoms appear randomly over the GaAs(ll0) terraces according to STM images. The adsorption sites are imaged as protrusions at negative bias and as depressions at positive bias (Stroscio et al., 1987b). This can be explained by the electronegative character of 0, leading to an enhanced DOS below EF and a reduced DOS above EF. In addition, there is an electrostatic effect involving the repulsion of conduction-band electrons by the negative 0. This results in a depletion layer around the 0, leading to band bending and thereby to a change in the DOS. Spectroscopic measurements show the disappearance of the dopant-induced peak, which is pinched off by the drastic reduction of transmission probability caused by the depletion layer (see Fig. 37). This also affects the topographic images up to 50 A away from the 0.

I o?

Io

-~

lo4

Io

-~ -4

-3

-2

-1

0

I

2

3

4

SAMPLE V O L I A G E ( V ) Fici. 37. Current-voltage measurements obtained on a clean GaAs(I10) surface (solid line) and on an oxygen-exposed surface (dashed line). The insets show schematic band diagrams for both surfaces. The different contributions to the tunnel current are indicated by C, conduction band, V, valence band, and D, dopant levels. [After Stroscio et al. (1987b).]

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The above results are contrasted by 0 adsorption on p-GaAs. At both positive and negative bias, spherical protrusions are observed at the adsorption sites, with less effect on the environment than in the case of n-GaAs (Stroscio et al., 1987c), indicating a minor role for band bending and thus a neutral 0.This can be accounted for by a negative-charge transfer from the 0 to the valence band, subsequently screened by an accumulation of holes (Stroscio and Feenstra, 1988).Since the protrusion has a diameter of only 5 A, the adsorption site can be determined, with the result that the 0 occupies a bridge position equidistant above one As and two Ga atoms. Another interesting case is the adsorption of Sb on CaAs( 1 lo), which leads to a (1 x 1) overlayer on top of the GaAs substrate (Feenstra and Mirtensson, 1988).Some defects in the form of missing or extra Sb atoms can be present. The Sb is thought to adsorb at the lattice sites of Ga and As, leading to two Sb atoms per unit cell. Three electrons of the Sb atom are used for bonding to the substrate, leading to one dangling bond left, filled with two electrons. This yields two valence band states, due to the inequivalent positions the Sb atoms occupy. These states were indeed observed in STM spectra, which showed peaks at 0.4eV and 1.4eV below the valence-band maximum (Mirtensson and Feenstra, 1988, 1989). The topography is also influenced by these states. At small negative bias, only one state is imaged, which leads to two maxima per unit cell. At large negative bias, the lowest-lying state determines the image, resulting in only one Sb per unit cell being imaged. Registration with respect to uncovered CaAs shows that these Sb atoms are bonded to the Ca. Tunneling to the empty states is associated with the back bonds between Sb and the substrate. Spectroscopic data show two peaks nearly equal in energy, 2.0 eV above the valence-band maximum. Other features in the spectrum are a slight shift of the Fermi level and the disappearance of the dopant-induced peaks, both indicating the presence of band bending. This band bending is largest on top of an Sb cluster. Spectroscopy at the edge of a Sb cluster reveals two new dangling-bond states around the Fermi level, which are probably responsible for the Fermi-level pinning. The GaAs(001) surface was studied by Pashley et a/. (1988b,c). Under standard growing and cleaning conditions the top layer consists of As, on which filled states are located. STM only shows good results at negative bias, thus probing this top layer. In that case topography leads to grooves parallel to the [TlO] direction, separated by 16.0 A, i.e., four lattice spacings. The elevated areas in between show a periodicity of 8.0 A in the [T 101 direction. Occasionally three separate maxima can be distinguished in the perpendicular direction inside the bright areas. A model to explain these results includes a dimerization along the [TlO] direction. A (2 x 4)unit cell then consists of a row of three dimers along the [1101 direction followed by one missing dimer. The missing dimers form the grooves in the [T 10) direction. Along the [Ilo]

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direction the unit cells can be in or out of phase, both geometries occurring in STM images.

3. Germanium Ge is in many aspects similar to Si. Molecular-beam epitaxy (MBE) of a layer of 500 A of Ge onto Si(ll1) shows the familiar (7 x 7) reconstruction (Becker et al., 1985d). However, after annealing the reconstruction changes into c(2 x 8), the equilibrium situation of Ge(l11).STM images show that this reconstruction is built up out of two smaller units, i.e., a (2 x 2) unit with one maximum and a c(4 x 2) unit with two maxima per unit cell. Both unit cells also exist independently on the Ge(l11) surface (Becker et al., 1985d). The various reconstructions are depicted in Fig. 38. The Ge(OO1) surface exhibits a (2 x 1) reconstruction, consisting of rows parallel to the [IT01 direction (Kubby et al., 1987). As with Si(001)(2 x l), a dimerization along the [ 110) direction can account for the rows. Contrary to the case of Si, the reconstruction on Ge is probably not defect-induced since the number of defects is very low. Because of buckling of the dimers, local p ( 2 x 2) or c(4 x 2) symmetries can arise, depending on the phase shift between neighboring rows. Spectroscopy reveals a band gap, surrounded by peaks at + 1.0 and - 1.0 eV, localized on the Ge atoms. Kubby et al. (1987) give a detailed theoretical model to explain the experimental results. Monoatomic steps are frequently observed, parallel to [I lo] or [loo], that lead to a change in orientation of the reconstruction by 90". The [loo] steps are

FIG. 38. Topographic images of a Ge(ll1) surface. (a) A mixture of (2 x 2), c(2 x 4) and c(2 x 8) reconstructed parts. (b)A single-domain c(2 x 8) area. The dotted lines indicate the periodic stacking of (2 x 2) and c(2 x 4) subunits that form the 4 2 x 8) unit cell. In both figures the unit cells are indicated by solid lines. [After Becker et al. (1988b3.3

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a!.

formed by missing dimers; the [110] steps occur in several shapes, depending on the participation in the dimer bonding of the atoms of the lower step edge. 4. Other Semiconductors Atomic resolution has been obtained on PbS(001), a polar semiconductor with a band gap of 0.4 eV (Zhenget al., 1988a).At positive bias both ions can be imaged, leading to two maxima per unit cell. Because of the filled character of the states located at the S z - sites, the maxima on these sites are more pronounced. At negative bias no imaging was possible, as a result of an electronegative tip (covered with S since S evaporates easily out of the PbS under vacuum), or of the n-type behavior of PbS. Some ceramic materials also exhibit semiconducting behavior, although the band gaps involved are generally high. Sufficient doping often makes successful STM imaging feasible. In this way Sic, with a band gap of 2.89 eV, could be imaged (Zheng et al., 1988b,c; Bonnell and Clarke, 1988)-even at low bias, according to the latter authors-because dopant levels are present in the band gap. Spectroscopy is possible because of the pinning of the Fermi level by these states. The opposite occurs at ZnO (band gap of 3.34 eV), where no states are available for Fermi-level pinning. Imaging is only possible at large negative bias, since the tunnel junction acts like a diode because of band bending.

C . Layered Materials

1. Graphite Graphite has become a very popular material for STM study. This is due to the easy preparation of an atomically flat surface over a large area, by simply cleaving the sample. The surface is also relatively inert, which makes feasible imaging in air (e.g.. Park and Quate, 1986; Bryant et al., 1986a) and in liquids (e.g., Sonnenfeld and Hansma, 1986; Schneir et al., 1986). Atomic resolution can be obtained easily, thus making graphite an ideal material for STM calibration. Extensive studies, however, have revealed several anomalous features, which clearly show that STM does not just image the total charge density. The first anomaly is the occurrence of “giant corrugations” within the unit cell, when the STM is operated in the topograhic mode. The corrugation grows with decreasing tunnel resistance (Mamin et al., 1986),and can take on values up to 24 a (Binnig et al., 1986a)on highly oriented pyrolitic graphite (HOPG), and even 175 A on a single crystal of graphite (Morita et al., 1988). These results can be partly explained by the peculiar electronic configuration of

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graphite (Mizes and Harrison, 1988).Graphite is a layered material with only small van der Waals forces between the layers. Inside one layer the C atoms are positioned in a honeycomb lattice formed by strong n bonds between the atoms. These n states are the only states at the Fermi surface and are located near the K points at the edge of the surface Brillouin zone of graphite, which gives rise to a nodal structure of the wave function (Tersoff, 1986). Since at small tunnel biases STM images only the states at the Fermi level, topographic images should show maxima at the C positions and a singular minimum at the center of the hexagons. However, because of smoothing by 1 # 0 tip states, imperfect instrumental response, interlayer effects, finite tunnel bias (Tersoff, 1986) and lattice vibrations (Leavens, 1988), the corrugation is finite and restricted to at most several angstroms. Soler et al. (1986) therefore proposed an additional effect due to elastic forces between tip and graphite. These forces, determined by the total charge density of both tip and sample, are important since the tip and the sample are in close proximity to each other because of the large effective tunnel barrier. The large barrier is the result of the parallel wave-vector component of the n bonds involved in the tunnel process. Because of the difference in LDOS (determining the tunnel current) and the total DOS (determining the interaction), the real corrugation is amplified by an additional deformation of the graphite lattice. A second effect is the creation of new surface states induced by the close presence of the tip, thus affecting the tunnel current (Ciraci and Batra, 1987). A deformation of the tip is also possible, since observations by Tiedje et al. (1988) indicate the presence of a carbonaceous layer on the tip after imaging graphite. The presence of such a layer is also desirable from a theoretical point of view in order to get similar states on tip and sample involved in the tunnel process (Stoll, 1988). Other effects that indicate the presence of a lattice deformation are the observed low work function (Mamin et al., 1986) and the fact that no feedback is required for a stable tunnel current (Smith et al., 1986b; Colton et al., 1988; Soethout et al., 1988). A problem with the force model is the large amount of elastic energy stored in the tip-graphite system, resulting in an unstable configuration in the case of a monoatomic tip. A larger contact area between tip and graphite with conservation of atomic resolution may be formed either by a flake of graphite dragged along with the tip (Pethica, 1986), or by a nonconducting contamination layer, where the tunnel tip breaks through (Mamin et al., 1986). An indication that the latter assumption is correct is the absence of a large corrugation when graphite is imaged in UHV after thorough annealing (Mamin et al., 1986). A second anomaly is the large asymmetry between adjacent C sites within the unit cell, resulting in only one maximum per unit cell-i.e., an apparent trigonal symmetry (see, for example, Park and Quate, 1986). This can be

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explained by also taking into account layer-layer interaction. The C sites in one layer are not equivalent. The ct sites have a C atom directly below in the second layer, whereas the p sites are situated above the center of a hexagon in the second layer. The 7t bonds at the c1 sites interact with the layer below, which leads to new bonding and antibonding states well away from the Fermi level. Thus STM only images the states at the p sites (Selloni et al., 1985; Batra et al., 1987; Tomanek et al., 1987). A third anomaly is the variety in shapes of the unit cell. An explanation in the form of tunneling from multiple tips was proposed by Mizes et al. (1987). Because of the elastic forces present between tip and graphite, several minitips can be at approximately equal distance from the graphite surface, each contributing to the tunnel current. The total STM image is then a superposition of single-tip images, shifted with respect to each other. When the tips image the same domain, the trigonal symmetry is conserved and only the apparent shape of the unit cell is changed. A change of tip during a scan thus leads to a change in unit-cell shape within one image (Soethout et al., 1988; see also Fig. 39). Simultaneous imaging of different domains, separated by a tilt boundary, leads to the observation of moire patterns (Albrecht et al., 1988a). Besides multiple tips, the size and the shape of a single tip will also influence the shape of the unit cell (Horie and Miyazaki, 1987; Mizutani et al., 1987).

FIG. 39. Grey-scale image of graphite, obtained in the current-imaging mode. Halfway through the image the apparent shape of the unit cell changes because of a sudden tip modification. [After Soethout et al. (1988).]

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Local spectroscopy on graphite (Reihl et al., 1986; Fuchs and Tosatti, 1987),showing the antibonding n* state at + 1.3 eV, a surface state at +2.5 eV and the bottom of the interlayer band at + 3.3 eV, agrees reasonably well with theoretical calculations (Selloni et al., 1985).The CJ bonds at -4.0 eV are not observed. Current-imaging tunneling spectroscopy (CITS) measurements (Bando et al., 1988)around +0.2 V and higher biases show current images in phase with the topographic image (obtained at a bias of -0.02 V), thus imaging the p sites. Filled states at the c( sites are imaged at biases below -0.2 V. A peculiar spectroscopic effect is observed when a defect, e.g., an adsorbed atom, is imaged (Bryant et al., 1986b; Soto, 1988). Far away from the surface the defect is imaged as a protrusion, whereas close to the surface only the periodic graphite structure is seen. In a model by Mizes and Harrison (1988), the defect introduces a wave function with a smaller parallel wave-vector component than in the case of pure graphite, thus being of more importance far away from the surface. Close to the surface the exponential distance dependence is of minor importance, and the larger prefactor of the graphite wave function determines the image. The theoretical framework of STM imaging of graphite can be tested further by considering graphite intercalation compounds (GICs). The main feature of these GICs is a shift of the Fermi energy with respect to the Fermi level in graphite. STM will therefore probe other states at low bias. Acceptor intercalants decrease E,, as is experimentally verified by spectroscopy on CoCI,-GIC (Tanaka et al., 1988).Donor intercalants increase EF.Theoretical work of Tomanek and Louie (1988)predicts a symmetric contribution of the C atoms to the STM image, since all sites are equivalent, a result of the AA stacking of the layers in most GICs. Explicit calculations of Selloni et al. (1988) on donor LiC, indicate a lowering of the corrugation with respect to the graphite case and differences between the hollow positions with or without Li below in the first intercalation layer. Experimental work on Lic6 (Anselmetti et al., 1988a), however, shows only several trigonal unit cells, among which is the normal graphite structure. Other donor and acceptor GICs also show only the graphite structure or no atomic structure at all (Anselmetti et al., 1988a; Gauthier et al., 1988). 2. Transition-Metal Dichalcogenides A second class of layered materials extensively studied with STM consists of the transition-metal dichalcogenides. Besides the atomic corrugation, STM images of many of these compounds show another periodicity, caused by charge density waves (CDWs). STM work on these materials at temperatures of 4.2 and 77 K has lately been reviewed by Coleman et al. (1988) and is only discussed very briefly here. The compounds studied in that paper-TaSe,, TaS,, NbSe,, VSe,, TiSe, and TiS,-exist in three phases, the trigonal

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FIG.40. Grey-scale image of 2H-TaSe, at 4.2 kelvin showing a CDW modulation superimposed on the atomic corrugation. The interatomic distance is a = 3.45 A; the CDW wave length is 3a. [After Giambattista et al. (1988).]

prismatic (1T) phase, the octahedral (2H) phase and a polytype phase consisting of an alternating stack of the former two phases (4Hb). In the 1T phase, the CDW transition has an onset above room temperature and involves a large charge transfer, thus leading to CDW corrugation dominating the STM image. The corrugation is enhanced by effects similar to those in the case of graphite. In the 2H phase, the atomic corrugation also plays a role in determining the STM image, because of the small charge transfer accompanying the CDW formation (see for example Fig. 40). The 4Hb phase shows either 1T or 2H behavior, depending on the termination layer at the surface. The structure observed with STM also depends on the tunnel bias, as shown by Tanaka et al. (1988),leading to atomic corrugation if the bias is inside the band gap created by the CDW transition, and to CDW corrugation otherwise. Compounds without a CDW transition were also investigated. Topographic measurements on MoS, show a hexagonal symmetry with one maximum (Stupian and Leung, 1987; Henson et al., 1988; Sarid et al., 1988)or two inequivalent maxima (Weimer et al., 1988) per unit cell. It is also not clear whether the main maxima are associated with S states of the top layer (Weimer et al., 1988) or with d,, orbitals of the subsurface Mo (Stupian and Leung, 1987). Hexagonal symmetry is also observed on GaSe (Humbert et al., 1987) and on WSe, and SnS, (Henson et al., 1988).

D. Superconductors Tunneling has always been an important technique for investigating superconductivity. Until the invention of the STM, experiments were restricted to solid-state tunnel junctions-i.e., metal-insulator-superconductor (MIS) junctions and superconductor-insulator-superconductor (SIS)junctions (see

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Hansma, 1982; Wolf, 1985).Because of the energy gap of 2A around the Fermi level, tunneling is prohibited when the bias is between - A l e and +Ale in a MIS junction and between -(Al + A2)/e and +(Al + A z ) / e in a SIS junction, 2A,,, being the energy gap of superconductor 1,2. At the gap edges the conductance (T = dl/dV diverges as a result of a singularity in the density of states of the superconductor. STM offers the possibility of investigating the spatial variations of the superconducting properties. Besides research on conventional superconductors, a lot of effort has recently been expended on the new high-T, superconductors. In addition, STMs and other piezoelectrically-driven devices have been used to study superconductor tunnel characteristics without scanning, especially on those materials out of which solid-state junctions cannot be made. This often leads to a point-contact geometry. Since in that case the surface topography or the spatial dependence of the superconducting properties is not determined, those last applications will not be discussed. 1. Low-T, Superconductors

The first spectroscopic STM measurements on a superconductor were performed by Elrod et al. (1984), who found a gap of 2A = 3.7 meV for a Nb,Sn thin film. On the same material a spatial imaging of (T(V = O)/a( V >> A) revealed patches of superconducting and of normal behavior (de Lozanne' et a/., 1985). The topography of an Nb film was investigated by Vazquez et a/. (1987c),showing that an increase of the roughness of the film is related to a decrease of the quality of tunnel spectra obtained when the film is used in an SIS junction. The topography of NbN shows a granular structure independent of the preparation conditions (Kirtley et a/., 1987; Marti et a/., 1987a). The first author also obtained the spatial variation of the band gap, which showed hardly any resemblance to the topography. STM can also be used to observe vortices, i.e., regions with a nonsuperconducting core in a type I1 superconductor. Dittrich and Heiden (1988) observed the motion of vortices in Nb. When these regions pass under the tip, the tunnel voltage drops when the current is kept constant. The first spatially resolved vortex patterns were obtained by Hess et al. (1989) on NbSe,. The vortices form a trigonal lattice with a lattice spacing depending on the applied magnetic field. Tunnel spectra in and around a single vortex show a strongly peaked conductance at the Fermi level in the center of the vortex, slowly turning into a BCS-like behavior at larger distances from the center. 2. High-T, Superconductors The recently discovered perovskitic superconductors are intensively studied with STM involving both topography and spectroscopy. The most

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important representatives are La1,85Sro.1 5Cu04-x (LSCO), YBa,Cu,O, - x (YBCO) and BiSrCaCu,O,. There are, however, several problems with studying these superconductors. Most research has been concentrated on superconducting ceramics and films, since single crystals are difficult to fabricate. Therefore most samples have a granular character, leading to inhomogeneities of the sample characteristics. Another problem is to what extent the bulk superconducting properties are conserved at the surface. Oxygen, crucial for the superconductivity, shows a rather large mobility, which leads to a lowering of the oxygen concentration in a surface layer of thickness 100-200 A. This makes the top layer insulating at low temperatures, thus causing mechanical contact between tip and sample upon tunneling. Volodin and Khailin (1987) therefore had to push the tip through this top layer in order to measure the spatial dependence of the energy gap of YBCO. To prevent severe damage to the sample, the tip was drawn back from the surface before each lateral movement. Among regions with a nearly constant gap, apart from small ridges and valleys, they also found superconductornormal boundaries where the gap collapses. All other papers are only concerned with topography, determined at room temperature where the surface appears semiconducting (Garcia et al., 1988) or even metallic (van de Leemput et al., 1988a,b). Many experiments are therefore performed at elevated voltages (Anselmetti et al., 1988b; Tang et al., 1988; Zheng et al., 1988b). Ceramics and thin films of YBCO (Jaklevic et al., 1988b; Laiho et al., 1988a; Niedermann and Fischer, 1988; Okoniewski et al., 1988; Vieira et al., 1988), BiSrCaCuO (Kirk et al., 1988a; Laiho et al., 1988b). TlCaBaCuO (Laiho et al., 1988b) and EuBaCuO (Anselmetti et al., 1988b) are found to possess a granular structure. Single crystals of YBCO (Heinzelmann et al., 1988a;van de Leemput et al., 1988a,b; Niedermann et al., 1989), HoBaCuO (Heinzelmann et al., 1988b) and BiSrCaCuO (Kirk et al., 1988a; Tang et al., 1988) show much less surface structure. On most surfaces steps with the dimension of the unit cell in the c direction are observed. In some cases lateral structure with atomic dimensions is also observed (Anselmetti et al., 1988b; Garcia et al., 1988; Laiho et al., 1988a), which is attributed to twin-domain boundaries. Repetitive one- or two-dimensional structure, with the periodicity of the underlying lattice (van de Leemput et al., 1988a,b; Okoniewski et al., 1988; Zheng et al., 1988b) or with a multiple of the lattice constant (Kirk et al., 1988a; Tang et al., 1988), is rarely seen. In all cases the corrugation is up to several angstroms, indicating a disturbed wave function at the Fermi level. E . Insulators

At first glance one might suppose that STM cannot be applied to insulators, since the large band gap leads to the absence of states around the

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Fermi level. Thus in order to reach the preset tunnel current the tip is easily driven into the sample, thereby making reproducible images impossible. However, states inside the band gap near the Fermi level can be introduced deliberately by defects in the form of dopant atoms, interstitials or vacancies. In this way images of S i c (Bonnell and Clarke, 1988) and of TiO, (Miranda ef al., 1985) can be obtained. Also, surface states may pin the Fermi level. Another way to bring states into the STM bias range is to shift the Fermi level near the conduction or valence band of the insulator. This can be attained by doping of the insulator or by growing a (thin) layer of the insulator onto a conducting substrate. The latter method is demonstrated by Wolkow and Avouris (1988b)on CaF, (band gap of 12 eV) deposited on Si(ll1). This yields a Fermi level only 3 eV below the conduction band of CaF,, making tunneling and imaging at positive bias possible. In a similar way, tunneling into the conduction band of NiO, on Ni(100) is possible (Garcia et al., 1986). A second problem involves the low density and the low mobility of the carriers inside the insulator. Insufficient conduction to or from the tunnel site leads to an accumulation of charge, which finally stops the tunnelling process. On partly oxidized Si(OOl),electron-trapping effects in isolated surface states can be observed (Welland and Koch, 1986; Koch and Hamers, 1987). When the tip is positioned above such a trap, the current becomes noisy and switches between two levels, which is associated with barrier changes caused by the trap being filled with an electron or being empty. As in semiconductors, band bending and the spreading resistance play an important role. Therefore the solutions discussed in Section V.B with respect to semiconductors (i.e., doping and thermal or optical excitation of electrons in the conduction band) may also apply in this case. Another solution which prevents or at least limits the accumulation of charge and does not require conduction through the insulator is the use of an ac tunnel current (Kochanski, 1989). By modulation of the bias with a frequency w in the GHz region and detection of the current at the triple frequency 3 0 (the current at w is eclipsed by stray-capacitance effects and the current at 2 0 is zero in a symmetric set-up), images could be taken of AI2O3and WSe,. When an insulating film covers a conducting material, it is sometimes possible to tunnel through the film directly into the substrate. The film should be rather thin in order to avoid mechanical contact between tip and film. An example is Ti, whose tunnel characteristics, obtained in air, show a band gap due to the presence of an oxide layer (Morita et al., 1986a). Tunneling at low voltages is believed to take place through the oxide, thus imaging the Ti surface itself, whereas images obtained at voltages above and below the gap of TiO, represent the TiO, surface. In the latter case there is much noise due to surface diffusion at the air-oxide interface. Evaporation of a conducting layer on top of the insulator is another possibility for obtaining information on the topography of the insulator.

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Spectroscopic information is lost in this way. Morita et al. (1986b) studied the oxide layer on Al. After removal of the Al, the oxide at the former Al-oxide interface could be imaged by using a Pt-Pd film (40-300A thick) as a conductive layer. Hemispherical close-packed structures were observed, in agreement with SEM images. Some structure, however, was attributed to the film itself. Jaklevic et al. (1988a) examined several insulators via evaporation of a thin layer of Au at 77 K. This method was shown to give smooth, continuous, very thin (50 A) films, very well representing the structure of the underlying insulator. An Au overlay was also used by Pappas et al. (1988)to study the roughness of A1203in a MIM junction in connection with surface-enhanced emission. Other ways to image insulators are the use of a replica technique or the use of atomic force microscopy (AFM), a technique closely related to STM (see Section V1.B).

F. Organic Molecules and Biological Materials The preceding sections showed that STM is capable of imaging various adsorbates on conducting substrates, often with atomic resolution. The next step is that STM may also be involved in imaging large organic molecules or even complete biological objects, when placed on a rigid conducting substrate. A short review of this field was recently given by Hansma et al. (1988). In contrast to conventional electron microscopy, the energy of the electrons involved in the imaging process in an STM setup is very low, implying nondestructive imaging. Another advantage is that STM is not restricted to vacuum. Tunneling in air or, even better, in liquids makes imaging in a natural environment feasible (see, for example, Lindsay and Barris, 1988; Wu and Lieber, 1988),which provides a minimal loss of shape of the molecules or biological objects. There are, however, several problems involving STM imaging of organic material. Unlike inorganic surfaces, where the atomic arrangement is generally well known in advance, the structure of organic material is very complex and often unknown, certainly when large molecules or biological objects are studied. Therefore most systems studied with STM, such as DNA and cell membranes, were already extensively studied with other techniques. Some model systems such as Langmuir- Blodgett films were also investigated. Another problem is the softness and flexibility of most biological materials, especially when fluids are contained. The sample is therefore easily elastically deformed, e.g., by an interaction with the tunnel tip. Also, Brownian motion and other thermal fluctuations can be larger than the features of interest. An example is the imaging of acetone vapor on HOPG, which yields rapidly changing images unless a complete monolayer of acetone is deposited

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(Hubacek et al., 1988).The substrate must therefore give sufficient support and anchoring to the sample. Another difficulty involves the localization and identification of the objects of interest. Since the scan range of the STM is limited, it is not possible to zoom in on the objects by using an increasing magnification. To restrict the searching time to an acceptable level, a sufficient number of objects must be attached to the substrate. O n the other hand, the objects should be kept separated to avoid distortion of the images by clustering. Identification of the objects requires a small corrugation of the substrate with respect to the dimensions of the object. Often HOPG and mica sputtered with PtC are used as a substrate, both giving rise to large atomically flat regions. A large-scan STM may be useful for identification and imaging of extended structures such as cell membranes (see, for example, Blackford et al., 1988). A more stringent problem, however, is the limited conductance of most organic and biological samples. One way to overcome this problem is to evaporate or sputter a thin metallic film (e.g., PtC) onto the sample. This technique has been applied to recA-DNA (Amrein et al., 1988;Travaglini et al., 1987,1988) and to sheaths of cell wall (Blackford et al., 1988).A second way is to make a replica of the sample, i.e., by depositing a metallic layer (e.g. PtC) onto the sample surface, followed by stripping or etching away of the sample. This technique can be used to image the inside of biological structures after fracturing at low temperatures, as demonstrated by Zasadzinski et al. (1988) on a biomembrane. Nevertheless, most research is performed by direct imaging of the organic or biological material. Sleator and Tycko (1988)reached atomic resolution on imaging the surface of a conducting organic molecular crystal consisting of tetrathiafulvalene-tetracyanoquino-dimethane(TTF-TCNQ). Often, ordered monolayers are imaged with atomic resolution. Co-adsorption of C6H6 and CO on Rh(ll1) gives a (3 x 3) periodicity (Ohtani et al., 1988; see Fig. 41) or a c ( 2 a x 4) periodicity (Chiang et al., 1988b). Acetone, a Re-carbonyl complex and dimethylsulfoxide on HOPG show periodic structure (Hubacek et al., 1988; Lyding et al., 1988b). In the same way, liquid crystals have been shown to form regular patterns on HOPG (Foster and Frommer, 1988).A lot of work has also been done on Langmuir-Blodgett films, often deposited on HOPG, most of which showed atomic resolution (Smith et al., 1987b; Albrecht et al., 1988b; Braun et al., 1988; Dovek et al., 1988b; Eng et al., 1988; Fuchs, 1988; Horber et al., 1988; Lang et al., 1988; Rabe et al., 1988; Wu and Lieber, 1988). Finally, large molecules or parts of biological material were imaged successfully at different degrees of resolution: recA-DNA (Travaglini et al., 1987, 1988), bare DNA (Barris et al., 1988; Lindsay and Barris, 1988; Beebe et al., 1989), amino acid chains and single amino acids (Feng et al., 1988a,b),cell membranes (Dahn et al., 1988; Stemmer et al., 1987)and parts of a bacteriophage (Baro et al., 1985, 1986).

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FIG.41. A three-dimensional view of Rh(111)(3 x 3)-(C,H, + 2CO). The benzene molecules can be seen as protrusions with a center dip, separated over 8.1 A. [After Ohtani et al. (1988).]

The tunneling and conduction mechanism is not clear in the case of direct imaging (Fuchs, 1988; Travaglini et al., 1988). For small molecules, tunneling can take place into localized conduction states hybridized with the conduction band of the substrate (see, for example, Gimzewski et al., 1987). For larger molecules, tunneling might occur to the surface of the molecules, followed by a conduction process such as hopping either through the film to the substrate or over the surface of the molecule(s). It is also possible that tunneling occurs through the molecule directly to the substrate (possible because of a low barrier height) or via a localized state in the molecule (resonant tunneling). G . Magnetic Materials

With the continuing development of data-storage technology, a growing interest exists in observation methods for magnetic-domain structures. STM is capable of investigating these structures in the nanometer region. Pure topographic information is obtained when magnetic material is sensed with a nonmagnetic tip. Corb et al. (1987) investigated a NdFeB compound in this way, which was rapidly quenched to obtain a fine-grain structure. Grains of 200 to 800 A in diameter were indeed observed. Barrier-height measurements indicated slight changes in chemical composition or a change in crystallographic orientation. The use of a ferromagnetic tip gives rise to a magnetic interaction between the magnetic moment of the tip m and the magnetic field due to the sample magnetization B. Since the force exerted on the tip is given by F = V(m B), STM will mainly be sensitive to changes in magnetization, i.e., domain walls (Saenz et al., 1987; Hartmann and Heiden, 1988). In this way a large (300 A)

-

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corrugation was observed on Fe at grain boundaries by using a CoCr tip, whereas the same surface showed only moderate structure when imaged with a W tip (Allenspach et a/., 1987). The mechanism behind the corrugation enhancement involves an elastic deformation of sample or tip and can therefore be better exploited with an atomic force microscope (AFM). A CoNi sample studied with an AFM using both a ferromagnetic and a paramagnetic tip shows the same behavior (Griitter et al., 1988). Another way to investigate magnetic properties is the use of spin-polarized electrons for tunneling, as was proposed by Meservey ( 1 988) and Pierce (1988). The tunnel current depends on the polarization of the electrons because the DOS of spin-up electrons of a magnetic sample differs from the DOS of spindown electrons. To separate topographic and spin-dependent information, the polarization of the tunneling electrons should be reversible. A second way is to probe the surface at several voltages, or to make a total spectrum in such a way that both spin-polarized states 'and spin-independent states are imaged. Several kinds of tips may generate polarized tunneling electrons. A ferromagnetic tip gives rise to a polarization of approximately 25%, at least when the surface is not contaminated. A superconducting tip may also be used in the presence of a magnetic field. Such a field causes Zeeman splitting, thereby shifting the energy of the unpaired electrons positively or negatively, depending on the polarization. This leads to electrons of nearly one spin at energies around the original superconductor energy-gap edges. Tunneling to a magnetic sample then gives rise to an asymmetric I - V characteristic, out of which the magnetization of the sample can be determined. Finally, an undoped semiconductor can be used as a tip. Electrons polarized up to 50% can be excited from the valence band into the conduction band by means of circularly polarized light. The polarization of the electrons can be inverted simply by reversing the polarization of the light. A third method for investigating magnetic materials is to use an STM as an electron source in the field emission region and to detect the spin polarization of the secondary electrons coming off the sample (Pierce, 1988). To avoid the capture of the low-energetic secondary electrons by the electric field of the tunnel junction, a sharp tip is required (Fink, 1988). Recently Allenspach and Bischof (1989) showed the first experimental results of this method. Secondary electrons coming off an FeBSiC sample showed a hysteresis of the spin polarization as a function of an applied magnetic field. The saturation value of 13% largely exceeds the theoretical expectations (McCord and Pease, 1987a).

H. Nanometer-Scale Surface ModiJcation The STM has lately generated much interest as a tool for modifying surfaces and fabricating structures on a very local scale. This is possible

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FIG.42. Indentation in an Ag(100)surface, caused by an excursion of the tunnel tip into the surface by a few hundred angstroms. [After van de Walle et al. (1986).]

because of the very small tunnel tip and the resulting small electron beam. One potential application is in high-density information storage devices (Thomson, 1988). The first way to induce a surface modification is by way of mechanical contact between tip and sample for a short time by driving the tip into the sample. Application of the technique to Au surfaces yields, in general, indentations 100-500 A wide (Abraham et al., 1986; Jaklevic and Elie, 1988; Packard et al., 1988).Small indentations are seen to disappear after some time, because of relaxation effects and diffusion. An Ag(100)surface was treated in a similar way by van de Walle et al. (1986), yielding a crater with a faceted structure (see Fig. 42). Since the Ag surface is much softer than the tungsten tip, the crater forms a fingerprint of the minitip responsible for the tunneling. An extensive study of the behavior near and at contact has been performed by Gimzewski and Moller (1987). Upon approach of an Ir tip to an Ag film, the tunnel barrier stays intact, confirming the theoretical results of Binnig e l al. (1984a) (see also Section 1I.B). Just before contact the resistance tends to saturate around 35 kR, in agreement with calculations of Lang (198713) for one-atom contacts. A protrusion is formed after the tip is driven more than 30 A into the surface. This is attributed to a strong adhesion between tip and sample, which results in a deposition of tip material upon retraction. For a contaminated tip the opposite effect is seen: the formation of an indentation while the contamination layer on the tip stays intact. A second way of nanomachining is to operate the STM at elevated current or bias. In general this is accompanied by a replacement of matter either on the sample surface or between the sample and the tip. This may be used, for instance, as a cleaning procedure for sample or tip (see e.g. Brunner et al., 1987;

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Emch et al., 1988~).The kind of modification (protrusion or indentation) is often unpredictable. Also, the precise mechanism of the change is generally not known. One mechanism for obtaining protrusions involves deposition of tip material onto the sample, especially when the tip is covered with sample material because of a previous contact between tip and sample. This might be the case for protrusions (100-200 A width) found on Au by Abraham et al. (1986) after a strong increase of the current and by Schneir et al. (1988a) after bias sweeps up to 3 V. Under similar circumstances, however, the latter group also finds hole formation. Holes of the same dimension (30-50 A diameter) were also observed by Emch et al. (1988~)after applying a voltage pulse of - 3 V. A very small protrusion (8 A diameter, 1 A height) was found by Becker er al. (1987) on Ge(lll)c(2 x 4) after a temporal bias of -4 V. Since the environment shows no change in structure, deposition of a tip atom is assumed. A second mechanism explains the structure modifications in terms of an increased energy dissipation by the tunneling electrons. The resulting heating of the sample at the tunnel site causes the sample to soften or even to melt locally. In this way Staufer et al. (1987) explain the formation of hillocks on flat Rh,,Zr,, after application of a bias of 2 V and a current of 300 nA. Also, Nagahara et al. (1988) attribute their observation of changes in Au at biases above 1.4 V to local heating effects. The electron beam of the STM can also be used to expose resist materials on top of a conducting substrate. These materials undergo a chemical change during the electron bombardment because of bond breaking, i.e., dissociation or polymerization. Albrecht et al. (1988b) imaged such an effect on an atomic scale: polymer fibrils on HOPG being disrupted or cut through by application of a voltage pulse (see Fig. 43). For a development process, discrimination is possible between exposed and unexposed resist areas. In this way structures can be written with STM on the order of 100-loo0 A, observable with electron microscopy and applicable for technological purposes. These structures are smaller than in conventional electron-beam lithography since the beam diameter is proportional to the applied bias, the latter being around 10 V in an STM set-up (McCord and Pease, 1987b). However, since many resists are insulators, a minimum bias is required to avoid tip crashing. A second effect limiting a further decrease of pattern width is the broadening of the exposed area caused by reflected electrons from the surface (McCord and Pease, 1987a). Reversal of the bias, such that the electrons tunnel out of the sample, reduces this effect. Work on several resists has been reported, including contamination resists (presumably hydrocarbons) on Si (McCord and Pease, 1986, 1987a; Ehrichs et a/., 1988a) and on PdalSi,, (Ringger et al., 1985), organic films on Si (McCord and Pease, 1986, 1988), and CaF, on Si (McCord and Pease, 1987b).

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FIG.43. Modification of polymer fibrils on HOPG with STM. A fibril, consisting of a bundle of polymer chains (a), has been disrupted or cut through at the location where the voltage pulse was applied (b). At a different location (c) along the same fibril, additional disruptures (d) are visible after two more pulses, applied at different points. The dimension of each image is 400 x 400 A2.[After Albrecht et al. (1988b3.1

A method similar to that described above uses the electron beam to dissociate molecules of an organometallic gas, yielding metal patterns on the sample (Ehrichs et al., 1988a,b; McCord et al., 1988).Analogously, Foster et al. (1988) showed that single organic molecules can be pinned at an HOPG surface out of a liquid by application of a voltage pulse. In a similar way, (partial) removal appears possible. A third method for surface modification is to use the STM tip as a liquidmetal ion source (LMIS). When the tip is covered with a layer of liquid metal-for example, Ga-ion emission will occur beyond a certain threshold bias, depending on the balance between electric-field stress and surface tension. Pioneering work in this field has been done by Ben Assayag et al. (1987), creating structures with minimum dimensions of several tens of microns. Smaller structures of tens of nanometers were obtained by Bell et al. (1988b) by using smaller currents (tens of nanoamps at a bias of 2 kV), which are possible because of sharper tips.

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1. Real-Time Observation of Dynamical Processes

Since STM is capable of imaging surfaces on an atomic scale, it should be possible to image time-dependent changes on surfaces. These changes may involve surface diffusion; adsorption and desorption of atoms, molecules or ions; or structural changes. Several groups investigated diffusion processes under UHV or ambient-air conditions. Diffusion of Au on UHV-cleaned Au( 11I) was studied by Jaklevic and Elie (1988).Indentations of 100-A diameter and two or three atomic layers deep, crea’ted by gentle touches of the tunnel tip, are filled in at a rate of a few atoms per minute at room temperature. Similar diffusion rates on Au( 11 1) were observed by Schneir et al. (1988a)after the creation of mounds or holes by means of a voltage pulse. In both studies no single atoms were observed. Ganz et al. (1989),however, were able to follow the motion of a five-atom Ag cluster on HOPG along a lower step edge. The motion could be described in terms of a one-dimensional random-walk hopping process. The relatively large number of events of zero displacement was attributed to the cluster-substrate interaction. During the diffusion changes inside the cluster were also observed, caused by rotation or self-diffusion. The above observations were shown to be independent of the presence of the tip. Some authors, however, see similar behavior under influence of the tip. Uozumi (1988) observed fast changes of the shape and position of thin Au islands 200 A in diameter on a cleaved MoS, surface. Besocke et al. (1988) studied dynamical processes in the step and terrace configurations on Si(OO1) that showed a general tendency to smooth the surface. The observed changes depended on the scan direction and on the scan time and are therefore influenced by the tip. A few groups investigated surface changes due to gas adsorption in a dynamical way. Ritter et al. (1987) observed the adsorption of CO, NO and C2H4 on clean Pt(100). Upon adsorption, the surface undergoes a transformation from a hexagonal to a bulk ( 1 x 1) reconstruction, leading to the explusion of excess Pt atoms in the form of islands. In the case of C O or NO adsorption, the islands arise at random positions, indicating a homogeneous nucleation for the adsorption. The adsorption of C2H4 occurs mainly at step edges (heterogeneous nucleation). The spatial progress of the reaction occurs predominantly via growth of already-existing (1 x 1) patches in one direction. Therefore, the growth rate exceeds the nucleation rate. The growth appears to be anisotropic, which is attributed to internal stress in the reconstructed Pt layer. Another reaction, the oxidation of Si( 111)(7 x 7), was investigated by Leibsle et al. (1988) on an atomic level. Upon oxidation the (7 x 7) reconstruction stays visible, the only effect being the disappearance of an adatom at the adsorption site. This observation of a depression is an electronic effect and does not mean the actual removal of the adatom. Already-existing

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defects act as a nucleation center for the oxidation. At a large coverage, the surface becomes disordered. Most surface reactions are imaged in an electrochemical cell under potentiostatic control. A review of the combination of STM and electrochemistry is given by Dovek et al. (1988~).We will restrict ourselves to electrochemical changes that take place over time in well-located areas. Uosaki and Kita (1989) followed the electrodeposition of Cu on polycrystalline Pt, leading to the growth of terraces and the filling of indentations. Preliminary measurements of van der Eerden et al. (1989) show electrolytic growth of Ag in an AgNO, solution. Green et al. (1988b)plated a Au(ll1) film with one monolayer of Pb, leading to growth of the islands and disappearance of the pits originally present on the surface. Apparently the step edges are enhanced-bonding sites. The Pb can be removed by the reversed process, yielding the original surface. Wiechers et al. (1988) imaged Au(ll1) in a chloride solution. After adsorption and subsequent desorption of 0.25 monolayers of C1-, there is a roughening of the step structures and a smoothing of the terraces, caused by a massive transport of Au over the surface during desorption. The opposite effect occurs in an oxidation-reduction cycle in a H,SO, solution, leading to a roughening of the terraces by the formation of islands of approximately 100 A width (Twomey et al., 1988). The oxidation-reduction cycle was also studied in HClO, by Trevor et al. (1989). They also find a roughening of the terraces, but in this case it is due to pits in the surface. The surface subsequently anneals in tens of minutes because of a motion of the pits around the terraces, until they fuse with the terrace edges or with each other. Addition of chloride to the solution leads to an enhanced step mobility, which involves a dissolution of Au. A similar phenomenon is observed by Otsuka and Iwasaki (1988) on roughened Au after an adsorption-reduction cycle of chloride. The structure of the surface changes dramatically because of enhanced surface diffusion of adatoms and clusters.

VI. RELATED SCANNING TECHNIQUES AND SPIN-OFF The success of STM opened perspectives to other kinds of scanning microscopies with a high resolution. Some techniques still use electrons tunneling from a sharp tip either to the sample or to the vacuum. Some technical devices were also developed in this area. Both are discussed briefly in the first section. A technique that only uses the concept of a scanning tip to obtain force images of a surface is the atomic force microscope (AFM).

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Since this technique is fast growing into a research field of its own, it will be discussed in a separate section. The rest of the microscopic techniques that use a tip but no tunneling electrons are briefly discussed in the last section. A . Tunneling Techniques

The first technique, scanning tunneling potentiometry (STP), is a modification of STM, allowing the measurement of both the topography and the electric-potential distribution of the sample surface. When a dc voltage is applied across the sample, the gradient of the potential along the surface will contain microscopic variations caused by inhomogeneities such as impurity atoms, vacancies, dislocations and grain boundaries. STP is able to locate such sites by providing a signal directly related to the local potential of the sample at the position of the tip. The first STP measurements were performed by Muralt and Pohl(l986). They used a regular STM setup with two electrodes on the sample such that a voltage difference AU = U, - U, can be applied over the sample (see Fig. 44). This results in a tunnel voltage Y(X9

Y) =

UI

+ U P kY )

(42)

at the position (x, y ) of the tip, when the tip is at virtual ground. Up is the local potential of the sample with respect to U , and contains the potentiometric information of interest. To separate the topographic and potentiometric data, at least two measurements are required. Muralt and Pohl (1986) use an additional ac voltage to separate both effects. The resulting ac component in the tunnel current is used to stabilize the tip-sample distance (via the lower feedback circuit in Fig. 44). In this way the topography is obtained. In the case of a semiconductor sample, a large ac voltage ( z 1 V ) is required to get a detectable ac current. The information on the potentiometry is contained in the dc tunnel current. Since the tunnel distances is kept constant, all variations in I,, are due to changes in Up. It is useful to install a second feedback system, which regulates I,, to zero by adapting the voltage U, (upper circuitry in Fig. 44).The potentiometric information can be obtained directly from the feedback signal U , , which is equal to - UP(x,y).Another advantage is that V, = 0, which implies that I,, is always evaluated on the same point of the I-U, characteristic. Otherwise a strongly nonlinear I - U, characteristic would make I,, also dependent on the local potential. Kirtley et al. (1988) followed a different technique, somewhat similar to current-imaging tunneling spectroscopy. The method only works well when

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u(x)

0

ELECTRODE 1

ELECTRODE 2

UZ Ibl

FIG.44. Principle of STP. (a) Potential distribution as a function of position on the surface, caused by an applied potential A U = U, - U, across the sample. The tunnel voltage between the tip (at virtual ground) and the sample is regulated to zero via an offset potential UREGL, applied to electrode 1. (b) Sample and feedback circuitry. The tunnel current is integrated by (I), providing the potential U,,,,. The ac part of the tunnel current, due to a modulation of the potential of electrode 1 by an oscillator (-) is fed to a lock-in amplifier (LI), a logarithmic amplifier (LG) and control circuitry (PI), the final signal being used for the distance regulation. [After Muralt and Pohl(1986).]

the tunneling characteristic is linear and the variations in local potential are small over the scanned area. Therefore, the second feedback system of Muralt and Pohl is not necessary here. The potential of electrode 1 can be switched between U1 and U , + V by an extra square-wave potential. U , is adjusted in such a way that the tunnel voltage V, in the absence of V is about zero compared to V. This assures that, after V is switched on, the adjustment of the tip-sample distance by the feedback system is not distorted by changes in local potential. The potentiometric information is obtained by measuring the tunnel current after the feedback is interrupted and V is switched off. The potentiometric measurement is performed at almost zero bias. This leads to a

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good signal-to-noise ratio, since the most important source of noise is fluctuations in tunnel resistance. The first potentiometric experiments were performed on a granular, partially discontinuous gold film (Muralt and Pohl, 1986). Because of the linear 1 - U, characteristic, the interpretation of the data is simple. The voltage across the sample (on the order of 5 V) was observed to drop almost entirely over a distance of about 100 A around grain boundaries, resulting in local field strengths of 108-109 V/m. This is in agreement with photoemission data. Also, Kirtley et al. (1988) investigated potential steps at grain boundaries of a polycrystalline AuPd film. They observed the same features on a smaller scale. The local potential at semiconductor surfaces was studied by Muralt (1986, 1987) on a GaAs p n junction and by Muralt et al. (1986b) and Muralt (1987) on a GaAs/AlGaAs heterostructure. The pn junction was forwardbiased and showed the main voltage drop occurring over a region of 150 A around the interface (Fig. 45). The voltage drop was slightly larger than the applied AU, because of the asymmetry of the tunnel characteristic. A small protrusion on the n side and a depression on the p side, both approximately 200 A away from the interface, were observed, indicating the presence of space-charge regions. In the case of the heterojunction, the voltage drop also occurred at the interfaces, with effects similar to those mentioned above. A second spin-off technique shows that STM imaging is not restricted to the determination of local vacuum-sample interface properties. Kaiser and Bell (1988) and Bell and Kaiser (1988) demonstrate that the Schottky barrier at a metal-semiconductor interface can also be probed. When a thin (100 A) metal film is deposited on a semiconductor surface a considerable amount of electrons, tunneling from the tip to the metal, can reach the metalsemiconductor interface without energy loss, since the attenuation length for electrons is metals is in the order of 100 A. When the tunnel bias is such that the energy of the incoming electrons exceeds the Schottky barrier height, a (collector) current through the semiconductor can be measured. This current as a function of bias is a measure of the interface electronic structure and of the bulk transmission through the metal, if the tunnel-barrier width is kept constant via the total tunnel current. The technique, which is called ballistic-electron emission microscopy (BEEM), was successfully applied to Au-Si( 100)and Au-GaAs(lOO), showing good agreement with theory. Another way to use the STM is in laser-frequency mixing (Arnold et al., 1987, 1988), using the fast time response of tunneling electrons in an STM geometry (time constant typically second). When the tunnel junction is irradiated with two laser beams, such as from a C 0 2 laser, the tip acts as a traveling-wave antenna, efficiently coupling radiation into the junction. The tunnel current then contains frequency components with the difference

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"REG

fAU

n

P

-A 200

-

X

FIG.45. Potentiometric (top) and topographic (bottom) image of the surface of a forwardbiased GaAs pn junction (AU = 0.5 V) around the interface. [After Muralt (1986).]

frequency of the two beams. The coupling mechanism is attributed to thermally assisted tunneling or to thermal expansion of the tip. The response signal of the STM depends on both the tunnel-barrier parameters and the beam parameters (polarization direction, angle of incidence, laser power and difference frequency). Therefore, laser-frequency mixing with an STM might be applied to local investigation of fast processes inside the junction-for example, the excitation of resonant states of molecules. Most surface-science techniques that use electrons as incoming particles can in principle also be applied to STM. By placing the appropriate detectors in the vicinity of the tunnel junction, secondary electrons or emitted radiation can be measured. In these cases the STM will be operated at elevated bias, i.e., in the field emission region with the tip as much as several hundred microns above the sample surface, in order to obtain incoming electrons in the correct energy range or to obtain a sufficient yield. In this way Reihl and Gimzewski

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(1987) detected secondary electrons to perform electron energy loss spectroscopy (EELS) and Auger electron spectroscopy (AES). Comparison with the respective conventional techniques shows some minor differences, probably caused by the strong inhomogeneous electric field around the tip. Fink (1988) used a 15-V incoming beam to detect topographic changes in the secondaryelectron yield. Variations with a lateral resolution of 30 A were observed on polycrystalline Au. Coombs et al. (1988) used STM to perform local inverse photoemission spectroscopy (IPS)in the region of visible light. This light is transmitted when the electrons, tunneling from tip to sample at voltages of 2-10 V, thermalize either to the Fermi level or to one of the image states at the sample surface (polycrystalline Ag in this case). Sweeping the bias voltage (i.e., the energy of the incoming electrons) and detecting light of one selected energy with a photomultiplier gives a well-resolved spectrum in which several image states can be seen. Another mode of operation is to detect at a fixed tunnel bias a complete optical spectrum with a spectrometer and an optical multichannel analyser. These spectra show broad peaks, whose positions do not shift with increasing tunnel bias. This is attributed to a resonant tunnel process involving surface plasmons as intermediate states (Gimzewski er al., 1989). As in surface-enhanced Raman scattering (SERS), this would explain the high quantum efficiency of the photon emission. Finally, we discuss two technical devices that incorporate an STM. An accelerometer has been developed by positioning the tip on a mass-loaded strip (Baski et al., 1988; Waltmann and Kaiser, 1989). When the device is submitted to an acceleration, the strip is deformed, which tends to change the barrier width. The resulting change of the feedback signal is proportional to the acceleration. Accelerations as small as 10-4g can be detected in this way. Miniaturization by fabrication based on chip technology opens the possibility of application in robots or in biomedicine. The second device is a magnetometer, developed by Wandass et al. (1989). In this setup the increase of an applied magnetic field causes the elongation of a metallic-glass ribbon with a large magnetomechanical coupling. The change in length is sensed with an STM. The highest accuracy is reached just before saturation of the ribbon, for which purpose a calibrated coil is placed around the ribbon. In the present setup, fields as low as 60 pG can be detected.

B. Atomic Force Microscopy

STM images are generally considered to contain only information on the electronic structure of the sample, convoluted in some way with electronic information of the tip. Sample and tip are assumed to be separated systems, not influenced by each other. However, several STM observations, such as

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extremely low barrier heights (Coombs and Pethica, 1986),giant corrugations on layered materials (Soler et al., 1986) and atomic resolution on (1 11) metal faces (Hallmark et al., 1987; Wintterlin et al., 1989) could only be understood by taking into account interaction forces between tip and sample. A first approach to explicit investigation of the interatomic forces between sample and tip was undertaken by Diirig et al. (1986a), who built an STM with the sample at the end of a cantilever. The lever is easily deformed by the interaction forces between sample and tip, which results in a corrugation enhancement at sites where the forces are large. Changes in the force between sample and tip will also cause a shift in the resonance frequency of the lever, which can be measured in the tunnel-current signal. In this way the existence of repulsive forces could be demonstrated. A drawback of this method is that it is difficult to distinguish between topographic and force effects. This problem was overcome by Binnig et al. (1986b),who designed the first real atomic force microscope (AFM). In this setup, a sharp tip is mounted on the end of a cantilever, while a sample can be scanned along that tip. The deflection of the lever is a direct measure of the force between sample and tip (see Fig. 46). The AFM is capable of detecting both repulsive (typically lo-' N ) and attractive, van der Waals (typically lo-" N) forces. However, operating in the repulsive region can damage sample and lever, since typical

FEEDBACK STM

,zm A

(b) A : AFM SAMPLE

B: AFM DIAMOND TIP

C: S T M TIP (Au)

U: CANTILEVER STM S A M P L ~ E : MODULATING-PIEZO

(AU-FOIL)u LEVER

F : VITON

FIG. 46. (a) Principle of AFM. A sample (A) is scanned along a sharp tip (B) on a cantilever (D). Because of interaction forces between the sample and the tip, the cantilever bends. This can be detected by an STM with tip (C), which uses the cantilever as a sample. The feedback signal can be applied to the piezoelectric z-drive of either the STM itself or the AFM sample, depending on the mode of operation (see text). Via the piezoelectric drive (E), a modulation can be applied to the lever. Viton spacers (F) are used for vibration decoupling. (b) Details of the cantilever. [After Binnig et al. (1986b).]

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chemical bonds have a strength of lo-' N. This may lead to rather blunt lever tips, since small minitips cannot sustain these large forces (Pethica and Oliver, 1987).In most cases this will cause a decrease of resolution. Also, the sample may change under the applied forces, leading to irreproducibility. Physisorbed molecules on a substrate will be especially sensitive to, for example, tip displacement. Therefore, biological samples should be investigated only in the attractive region (Persson, 1987). Because of the magnitude of the forces involved, the cantilever should have a small force constant to get a measurable response. There is, however, a lower bound to the value of this force constant. The amplitude of the thermally activated excitation of the lever increases with decreasing force constant. For a good signal-to-nose ratio and a low risk of damaging sample or lever, this amplitude should be small compared to the average distance between sample and lever. Besides, small force constants lead to unstable lever positions when the lever is approaching the sample (McClelland et al., 1987). Typical values for the force constant are 10-2-102 N/m. In addition, a high mechanical resonance frequency is advantageous for obtaining efficient decoupling from outside vibrations and a reasonable scan speed. This leads to levers that are as small as possible. Typical resonance frequencies are in the range of 10-50 kHz. There are several techniques for fabricating the levers. The first AFMs used metal foil on which a diamond tip was glued (Binnig et al., 1986b; Heinzelmann et al., 1987). Metal wires, etched to a sharp tip, are also used (Erlandsson et al., 1988; Mate et al., 1987), or cross wires and a diamond tip (Marti et al., 1987b). Finally, microfabricated structures of SiO, are used, occasionally with a diamond or an evaporated tip at the end (Albrecht and Quate, 1987, 1988). The deflection of the lever can be detected in various ways: By STM, which monitors the distance between the tip and the back of the lever (Binnig et al., 1986b, 1987; Albrecht and Quate, 1987, 1988; Heinzelmann et al., 1987; Marti et al., 1987b; Yamada et al., 1988). The feedback signal can be applied to the piezoelectric z-drive of either the sample or the STM (see Fig. 46). By optical interferometry between a laser beam and its reflection by the back of the lever (Martin et al., 1987; Erlandsson et al., 1988). This optical method is more reliable and easier to implement than detection by tunneling, because of its low sensitivity to the roughness of the lever and to thermal drift (McClelland et al., 1987). By optical deflection of a laser beam, reflected by a tiny mirror on the lever (Meyer and Amer, 1988). By capacitive techniques (Mate et al., 1988).

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Apart from the detection mechanism of the lever deflection, there are several modes of operatioh: The constant-force mode. The lever deflection is kept constant by adjusting the z position of the sample. In this case, the AFM follows contours of constant force. Forces as weak as lo-’’ N can be detected in this way, restricting this method to the strong repulsive interaction between sample and lever. An increase in the scan speed is possible by keeping only the average deflection constant. The force information is then contained in the variations of the tunnel current or the light intensity. The “STM” mode (only applicable in the case of STM detection). The z position of the STM tip is adjusted, as in normal STM operation (Heinzelmann et al., 1988~). The AFM is easier to operate, but the constantforce condition is abandoned. The constant-force derivative mode. When the sample is modulated in the z direction, the lever is forced into a harmonic oscillation via their mutual interaction. If a feedback signal is used that keeps the amplitude of the lever oscillation constant, contours of constant force derivative are imaged (Erlandsson et a/., 1988). With this method the weak attractive forces can also be studied. The modulated-lever mode. The resonance frequency of the free lever will shift because of the sample-lever interaction, the magnitude of the shift determined by the force derivative (Erlandsson et al., 1988).By modulating the lever at resonance, the shift can be observed via a change of the magnitude or the phase of the lever oscillation. The sensitivity of the method is determined by the quality factor of the resonance (Martin et al., 1987). A variety of experiments already have been performed with AFM. There is no restriction on the environment in which the AFM is operated. Most experiments have been performed in ambient air, but some also in liquids (Marti et al., 1987b) and at cryogenic temperatures (Kirk et al., 1988b). The great advantage of AFM with respect to STM is that nonconducting surfaces can also be studied. Several insulators have been imaged: highly oriented pyrolitic BN (HOPBN) by Albrecht and Quate (1987, 1988) even at atomic resolution; quartz by Heinzelmann et al. (1988~);LiF by Heinzelmann et al. (1988~) and Meyer et al. (1988); NaCl by Marti et al. (1987b) in paraffin oil; and oxidized Si by Marti et al. (1 988a). High-T, superconductors have been investigated by Heinzelmann et al. (1988a). In addition to HOPBN, atomic resolution has also been obtained on HOPG by Albrecht and Quate (1987, 1988), Marti et al. (1987b), Erlandsson et al. (1988) and Yamada et al. (1988), and on 2H-MoS2 by Marti et al.

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(1987b). At present atomic resolution is only obtained in the repulsive-force region on layered materials. The mechanism for the high resolution is more likely caused by a sliding of basal planes in the sample, which gives a coherent contribution to the experienced force (Pethica, 1986; Soler et al., 1986), rather than by a sharp tip, which is not stable under these large forces (Pethica and Oliver, 1987). Atomic resolution in the attractive region is difficult to obtain, since a large part of the tip is involved in the imaging because of the long-range behavior of the interatomic forces (asY2 in the case of a spherical tip and a flat surface; see McClelland et al., 1987).A quantitative comparison between the resolution in an STM and in an AFM set-up can be made when the AFM can also operate in STM mode (Bryant et al., 1988; Marti et al., 1988b). Several special forces can be examined with AFM. During force imaging in the repulsive region, large hysteresis effects are sometimes observed, leading to a substantial distortion of the unit cell. These are caused by lateral friction forces formed by dragging the tip along the surface. By a slight modification of the AFM setup, these forces can also be investigated explicitly, even with atomic resolution (Mate et a/., 1987; Kaneko et al., 1988). When a potential difference is applied between sample and lever, an attractive force is automatically created. In this way the local electrostatic potential and capacitance can be measured (Erlandsson et al., 1988; Martin et al., 1988a). Magnetic forces can be imaged by using a magnetized tip. This was investigated by Saenz et u1. (1987), who also developed a theory for magnetic imaging, and by Abraham et al. (1988), Grutter et al. (1988), Martin and Wickramasinghe (1987), Martin et al. (1988b) and Wickramasinghe and Martin (1988). C . Other Nontunneling Techniques

The first technique to be discussed is scanning near-field optical microscopy (SNOM), which images the optical properties of a sample with a resolution of 10 nm. The technique is not restricted to conducting surfaces and can be applied under ambient-air conditions. The probe consists of a quartz slide or tip, covered with a metallic layer (typically 1000 nm thick). A small hole in this layer, with dimensions of approximately 10 nm, serves as an aperture. When a laser beam irradiates the aperture, the light that is transmitted through the aperture will have an evanescent character, since the aperture size is much smaller than the wavelength of the incoming light. When an absorbing medium (i.e. the sample) is scanned at close distance across the aperture, information can be obtained on the optical properties of the medium by

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FIG.47. Principle of SNOM. A quartz tip, coated with a metal film, is positioned in close proximity to the sample surface. A small aperture at the top of the tip transmits light to the sample. This radiation interacts with the sample in the near-field zone. The light, transmitted through the sample or back-scattered into the tip, is detected by a photomultiplier. The tunnel current between tip and sample can be used to keep the distance constant. Copyright 1986 by International Business Machines Corporation; reprinted with permission. [After Diirig et al. (1986b).]

detecting the scattered radiation with a photomultiplier (see Fig. 47). In the first SNOM designs, the forward-scattered radiation was detected (Pohl et al., 1984:Durig et al., 1986b,c;Pohl et al., 1988),which has the drawback that the sample must be transparent, i.e., thin compared to the penetration depth of the light. Therefore it is more usual to detect the backward-scattered radiation that is reflected back into the probe (Fischer et al., 1987,1988; Pohl et al., 1988). The resolution of the SNOM is determined by the aperture size and the distance between sample and probe. The minimum aperture size is approximately 10 nm, determined by the sharpness of its boundaries and by the detection sensitivity of the photomultiplier. The distance between sample and probe should be as small as possible, on the order of the aperture diameter. The stability of the distance is also important, since the influence of the sample on the scattered light depends strongly on this distance. The distance can be controlled with an STM setup by covering both the probe and the sample with a thin (smaller than the skin depth) transparent metal film. Also, the photomultiplier signal can be used for stabilization. Most experiments until now have been performed on glass.samples, partly covered with a metal. By this means, strong contrast differences can be expected between the transparent and the opaque parts of the sample. This works in both the transmission and the reflection mode of operation. SNOM may be used as a spectroscopic tool by adjusting the frequency of the incoming light to a vibrational mode of the sample (Pohl et al., 1988).

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Another technique is scanning thermal microscopy, developed by Williams and Wickramasinghe (1986). The tip consists of a small thermocouple element (1000 A in diameter), able to detect temperature changes of 0.1 mK. When the tip, which is heated, is in the proximity of a sample (micron range), its temperature decreases slightly because of the thermal coupling between the tip and the sample. The mechanism of the coupling is via thermally excited electric fields close to the sample and tip surfaces, according to Dransfeld and Xu (1988). This leads to a strong distance dependence, which makes the temperature loss an excellent measure of the distance. In practice, the tipsample distance is modulated and the resulting ac thermocouple signal is used for feedback in order to avoid thermal-drift effects. In this way topographic images with 30-A perpendicular and 1000-A lateral resolution can be obtained. To obtain independently a temperature map of the surface, the sample temperature can be modulated at a second frequency. The corresponding thermocouple signal is a measure of the temperature variations of the sample (Martin et al., 1988~). Finally, two microscopic techniques that operate in electrolytic solutions are discussed. The scanning electrochemical microscope uses the faradaic current for stabilization of the tip-sample distance (Bard et al., 1989). The resulting image combines topographic information and electrical and chemical properties of the sample. The technique can also be used for local modification of surfaces-for example, by photoelectrochemical etching (Lin et al., 1987). In scanning ion-conductance microscopy, a micropipette filled with an electrolyte scans the surface. The conductance between micropipette and sample depends on the cross-section of the ion path and thus on the distance between micropipette and sample (Hansma et al., 1989). The topographic resolution depends on the micropipette opening but can be as small as 1000 A.

ACKNOWLEDGMENTS The authors thank Dr. Th.H.M. Rasing for critical reading of the manuscript. This work was part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) and was made possible by the financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO).

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ADVANCES I N ELECTRONICS A N D ELECTRON PHYSICS. VOL 79

Phosphor Materials for Cathode-Ray Tubes TAKASHI HASE

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Techntcal Department Kasei Optonix Ltd Kanayawa. Japan

TSUYOSHI KANO Central Research Laboratory. Hi tachi Ltd Tohyo. Japan

EIICHIRO NAKAZAWA* N H K Science and Technical Research Lahoratories. Japan Broadcasting Corporation Tokyo. Japan

HAJIME YAMAMOTO Central Research Lahoratory. Efitachi Ltd . Tokyo. Japan 1. Introduction . . . . . . . . . . . . . . . . . . . . . I1. Luminescent Processes of Phosphors . . . . . . . . . . . A . Light Generation . . . . . . . . . . . . . . . . . . B. Quenching of Luminescence . . . . . . . . . . . . . C. Decay Processes . . . . . . . . . . . . . . . . . . Ill . Cathode-Ray Excitation Processes . . . . . . . . . . . . A . lnteraction of Incident Electrons with the Surface of a Solid . . B. Phenomenological Description of Electron Penetration . . . . C. Elementary Processes Resulting from Cathode-Ray Excitation . D . Host Sensitization . . . . . . . . . . . . . . . . . . E. Cathodoluminescence Efficiency . . . . . . . . . . . . I V . Phosphor Materials for Specific Applications . . . . . . . . . A . Television. . . . . . . . . . . . . . . . . . . . . B. Terminal Displays . . . . . . . . . . . . . . . . . . C. Cotor Projection Displays . . . . . . . . . . . . . . D . Oscilloscope Tubes . . . . . . . . . . . . . . . . . E. Tubes for Special Applications Requiring Very Short Persistence . F . Vacuum Fluorescent Displays . . . . . . . . . . . . . G . RadarTubes . . . . . . . . . . . . . . . . . . . . H . Flood-Beam Storage Tubes . . . . . . . . . . . . . I . Special Applications Requiring High-Resolution Screens . . . J . Small Monochrome Tubes . . . . . . . . . . . . . . V . Methods Used for Synthesis of Phosphor Powders . . . . . . . A . General Procedures . . . . . . . . . . . . . . . . . B. Preparation of Some Widely Used Phosphors . . . . . . .

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* Currently at the Electronic Engineering Division. Kogakuin University, Hachioji, Japan . 27 I

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VI. Screen Fabrication Techniques. . . . . . . . . . . . . . . . . A. Settling Method . . . , . . . . . . . . . . . . . . . . B. Slurry Method . , . . , , . . . . . . . , . . . . . . . C. Dusting Method . . . , , , . . . . . . . . . . . . . . D. Electrophoretic Method. . . . . . . . . . . . . . . . . . VII. Special Phosphor Screens , . . . . . . . . . . . . . . . . . A. Voltage- or Current-Density-Controlled Multicolor Screens . . . . . B. Thin-Film Screens. . . . . . . . . . . . . . . . . . . . VIII. Phosphor Aging. . . . . . . . . . . . . . . . . . . . . . A. Background. . . . . . , , . . . . . . . . . . . . . . B. Factors Involved in Aging . . . . . . . . . . . . . . . . . C. Browning of Glass. . . . . . . . . . . . . . . . . . . . IX. Contrast-Enhancing Techniques in Color Tubes. . . . . . . . . . . A. Nonglare Glasses . . . . , . . . . . . . . . . . . . . . B. Black-Matrix Screen . . , . . . . . . . . . . . . . . . . C. Pigmented Phosphors , , . . . . . . . . . . . . . . . . X. Conclusion . . . . . . . . . . . . . . . . . . . . . . . Acknowledgment . . . . . . . . . . . . . . . . . . . . . Appendix 1. Characteristics of Widely Used Phosphors for Main Categories of Cathode-Ray Tubes . . . . . . , , . . . . . . . . . . . , Appendix 2. Relative Spectral Distribution Curves of Cathodoluminescence Emission for the Phosphors Listed in Appendix I. . . . . . . . . . . References

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332 333 334 336 337 337 337 341 349 349 3 50 351 353 3 54 355 355 3 56 358

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INTRODUCTION'

The cathode-ray tube (CRT) was invented by Karl Ferdinand Braun in 1897 for displaying electrical signals. Although primitive by today's standards, its usefulness could be demonstrated readily because of the availability at the time of a few naturally occurring luminescent minerals such as willemite (Zn,SiO,) and scheelite (CaWO,). These were already known to fluoresce strongly in a gas discharge environment (excited either by UV or energetic electrons) and, deposited as a thin powder layer on a mica substrate, served as the viewing screen of the early tubes. Although it had been known some years before the invention of the CRT that stable phosphors, such as ZnS, could be synthesized in the laboratory and that trace elements were required to make a phosphor luminescent, research on phosphor materials was limited until about 1930, when it became clear that the CRT was ideally suited for displaying television images. For this purpose there was particular emphasis on obtaining phosphors with suitable spectral distribution for monochrome television and whose persistence was sufficiently short. Further research was stimulated during the 1940s by the need for phosphor screens with the very long persistence required for radar appliBy T. Kano

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cations. Since then the additional requirements of color television, computer terminals and oscilloscopes, as well as the special requirements of industrial and military display systems, have resulted in extensive research and development work on new phosphors that has continued to the present. Despite the progress made during the past 10 to 15 years in other display technologies, such as liquid-crystal devices, gas panels and electroluminescent panels, the versatility and level of performance reached by the cathode-ray tube remain in most cases as the criteria by which most other displays are measured. The unusual status of the cathode-ray tube is, in turn, attributable in large degree to the high performance levels achieved with modern phosphor materials. Among these are their high efficiency (as high as 20%) in converting electron-beam energy to light, their extraordinarily high peak brightness (which may be greater than lo7 cd/m2), their long life (many thousands of hours), the wide choice of emission colors, the great range of decay times (from less than seconds to greater than 1 second) and, not least, the ease with which large-area uniform layers can be deposited. In the following chapter, the basic luminescent processes are first discussed in Section 11. In Section 111 the specific excitation processes occurring under electron bombardment are then considered. This is followed by a discussion in Section IV of phosphor materials for specific applications. In Section V methods for the synthesis of phosphors are described, and in Section VI screen fabrication techniques are discussed, while in Section VII phosphor screens with special properties are described. In Section VIII the processes involved in the aging of phosphors are discussed, and in Section IX methods for enhancing the image contrast of phosphor screens are treated. In the appendixes, the characteristics of widely used phosphors and their emission spectra are listed separately.

11. LUMINESCENT PROCESSES

OF PHOSPHORS’

Luminescence is defined as a phenomenon whereby the emission of light occurs in excess of thermal radiation. The luminescence may be induced not only by the absorption of external light (photoluminescence) or the kinetic energy of electrons (cathodoluminescence), but also as the result of other types of excitation, such as applied electric fields or currents, chemical reaction, and the incidence of high-energy particles. (For general references on luminescence see Kroeger, 1948; Garlick, 1949; Leverenz, 1950; Curie, 1963; Goldberg, 1966.) By E. Nakazawa

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A. Light Generation

1. Phosphors

A microcrystalline material manufactured to make practical use of its luminescent property is called a phosphor. Usually phosphors are in the form of a powder, but in some cases they may be in the form of a thin film. Most cathode-ray tube (CRT) phosphors are synthesized by intentionally introducing an impurity with a concentration of 10’9-1021 cm-, into an inorganic crystalline powder. The impurity that activates the crystal to luminesce is referred to as an activator, while the crystal itself is referred to as the host or matrix. A phosphor is usually identified by its chemical formula, as in the case of ZnS: Mn, for example, where ZnS is the host and Mn is the activator. The host material of CRT phosphors should have a wide band gap and be transparent enough to enable the transfer of visible light to the surface of the powder crystallites. From a practical point of view, the host must be chemically stable in the presence of water since it is usually suspended in an aqueous solution during the screen deposition process. It must also be thermally stable since the CRT glass envelope must be baked at temperatures up to 250-350°C in vacuum in order to be outgassed. Sulfides (ZnS, CdS), oxysulfides (Y 20,S, Gd,O,S), silicates (Zn,SiO,, Y ,SiO,), and aluminates (Y,A1,012, YAIO,) are the principal hosts of currently used CRT phosphors. Since some kinds of transition metal ion impurities (Fe, Ni, Co) reduce the emission intensity of phosphors, the host crystal must be manufactured carefully so as not to include more than one ppm (10’’ cm-,) of these impurities. Problems associated with environmental pollution must also be considered in selecting materials for phosphors. For example, CdS, a useful material for sulfide phosphors, is being avoided in Japan since it is suspected to be harmful to the human body. 2. Activators and Luminescent Centers When an energetic electron, accelerated, for example, to 6 keV or more, enters an inorganic crystal, hundreds of free electrons and free holes are produced along the path of the incident electron. If the crystal is perfect, that is, free from impurities and lattice defects, the free electrons and holes created in the conduction and valence bands, respectively, may directly recombine as represented by (a) in Fig. 1, emitting luminescence, the energy of the photon being equal to the band gap between the valence and conduction bands. This intrinsic emission due to the “band-to-band’’ transition is rarely found in CRT phosphors, the only case being the ultraviolet emission band of ZnO phosphor used in flying-spot tubes (Miyamoto, 1978).

-iI

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES

j

je

a

b

c

-Y-

I

,

I

j

:

\.

j

I

v

275

V

,

’,

..__I’

FIG.I . Models of luminescent transitions. (a) Direct recombination of a free electron and a hole (band-to-band transition); (b) transition of a free electron to an acceptor level (Riehl-Schoen-Klasens model); (c) recombination transition of a donor electron with a free hole (Lamb-Klick model); (d) transition between a donor and an acceptor (Prener-Williams model); (e) transition within a localized luminescent center.

The crystal of CRT phosphors generally contains activator impurities as well as incidental impurities and lattice defects (see Shionoya, 1966). These imperfections distort the crystal lattice and create localized energy levels in the band gap, providing effective recombination paths for the excited electrons and holes, as represented by transitions (b), (c), and (d) in Fig. 1. These transitions, overwhelming the direct transition (a), emit light whose photon energy is smaller than the band gap in accordance with the depths of these levels. Cu and Ag activators in ZnS:Cu, A1 and ZnS:Ag, CI phosphors, for example, produce deep acceptor levels with different depths. These capture a free hole that will then radiatively recombine with an electron captured by a shallow donor level produced by a CI or Al atom, as shown by (d) in Fig. 1, thereby emitting a photon whose energy is equal to the band gap minus the depths of the acceptor and the donor levels. The rather large difference of the depths of Cu and Ag acceptor levels, 1.25 eV and 0.72 eV, is the main cause for the different emission colors of the phosphors, i.e., green and blue, respectively. In accordance with the choice of activator, one can thus obtain luminescent emission of many different colors with a given host crystal. The model of transition (b) in Fig. 1, i.e. the transition between the conduction band (a free electron) and a deep acceptor, was first proposed by Riehl, Schoen and Klasens (see Curie, 1963) for the blue and green luminescence of Ag and Cu activators in ZnS hosts. However, this was replaced later by model (d) for these activators. Model (c), referred to as the Lamb-Click model, represents the reverse situation of model (b), that is, a transition between a deep donor and the valence band (a free hole). However, it is rarely found to occur in CRT phosphors. Model (e) corresponds to an intraatom or intramolecule transition, that is, the transition occurring in a welllocalized luminescent center such as a rare-earth or transition-metal ion

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(Eu3+,Ce3+,Mn2+)or a molecular complex of atoms, with the electrons confined to the same small center before and after the transition.

3. Coactivator and Charge Compensator In a sulfide phosphor such as ZnS:Cu, A1 and ZnS:Ag, C1, the dopant of a VIIb-group element (halogen; C1, Br, I ) or a IIIb-group element (Ga, Al) is referred to as a “coactivator” since the intensity of emission can be greatly increased by the addition of about the same amount of coactivator as activator, while not changing the emission color, which remains independent of the kind of coactivator used. From these features Kroeger et al. (1949) deduced that the role of the coactivators in ZnS phosphors was to compensate for the excess minus charge caused by the substitution of a Cu+ or Ag+ activator ion for a Zn2+lattice ion. This compensation is accomplished by the plus charge produced by the substitution of, for example, an A13+ or C1- ion for a Zn2+ or S2- ion, respectively, thereby keeping the charge neutrality of the whole crystal. The coactivation by means of charge compensators generally results in a more uniform distribution of the activator ions, thereby extending the concentration of activator that can be incorporated in the host. Another important role of the coactivators in sulfide phosphors, involving the concept of donor-acceptor (D-A) pair emission, was suggested by Prener and Williams (1956). Later Shionoya and coworkers (Era et al., 1968) presented experimental evidence for this based on the theoretical analysis of D-A pair emission by Hopfield et al. (1963).The following subsection will deal with the details of this type of emission. 4. Donor- Acceptor Pair Emission and Self- Activated Emission In a ZnS:Cu, A1 phosphor both the Cu’ and AI3+ ions are substituted for Zn2+ions, with the excess charges around the ions being compensated by each other. While the A1 coactivator produces a donor level in ZnS hosts, the donor electron is, as a result of the charge compensation, transferred to the deep Cu acceptor level. Hence, both the donor and the acceptor are ionized in the ground state of the system. Free electrons and holes produced in the bands by excitation are therefore rapidly captured by the ionized donor and acceptor, respectively, and neutralize them. Then, determined by the lifetime of these states, the captured electron at the A1 donor will be transferred radiatively to the Cu acceptor and recombine with the hole therein, as represented by the transition (d) in Fig. 1. The lifetime of the captured electron, which is equal to the inverse of the radiative transition probability, is a function of the separation r between the donor and the acceptor, since the transition is induced by the overlapping of electron clouds between them. The radiative

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transition probability W ( r )and the transition energy E ( r ) of a donor-acceptor pair were given by Hopfield et al. ( 1 963) as W ( r ) = W(O)exp(- 2r/rH), E(r) = E ,

-

E D - EA

+ e2/Er,

where rRis an effective Bohr radius, E , the band gap, 1: the dielectric constant of the host, and E D and EA are the binding energies of the donor and acceptor, respectively. While both the donor and the acceptor are neutralized in the initial state of the transition, they are ionized in the final state, thereby making the energy of Coulomb interaction different before and after the transition. This causes a Coulomb energy-dependent term in the transition energy, E(r), in Eq. (2). Since the Coulomb energy naturally depends on the pair separation, pairs composed of the same kinds of donor and acceptor atoms, but having different pair separation distances, will have different transition energies. The spectrum of this type of emission, referred to as donor-acceptor (DA) pair emission, often shows a peculiar time dependence caused by the pairseparation dependence of the transition probability and emission energy. The emission of ZnS:Cu, Al and ZnS:Ag, CI, two of the most important CRT phosphors, occurs from this type of transition (Era er ul., 1968). Suppose that the AI(CI) donors and Cu(Ag) acceptors are randomly distributed in these phosphors, and hence, the AI-Cu pair separation ( r )is distributed over a range of values; the entire emission spectrum, which is composed of the spectra distributed in accordance with the different emission energies and timedependences given by Eqs. (1) and (2), changes in shape with the excitation intensity and the time after excitation since the spectral distribution will change with these two variables. Such peculiar time- and excitationdependent spectra were observed in the case of the green emission of ZnS:Cu, CI(AI) and the blue emission of ZnS:Ag, CI (Era et al., 1968). Since a strong electron-phonon coupling is expected for a deep level such as that of Cu and Ag acceptors (Section 11.A.6), the emission spectrum corresponding to each D-A pair would have a broad vibronic width even at a very low temperature, resulting in a very broad D-A pair spectrum whose peak changes its position as a function of the excitation intensity and the time after excitation. By comparison, the emission called “edge emission”, appearing close to the absorption edge of rather pure ZnS and CdS, corresponds to shallow D-A pair emission. Since the electron-phonon coupling is weak for such shallow donors and acceptors at low temperature (Section 11.A.6),the spectrum of this emission at low temperature is composed of many sharp lines, each line corresponding to a different pair separation.

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In the case of sulfide phosphors without any activator, doping them with coactivators (CI, Al, Ga, Br, I or In) can induce emission, whose color is almost independent of the coactivator species, e.g., blue emission in ZnS. This emission is referred to as “self-activated,” and in many cases it shows the characteristic time and excitation dependence of D-A pair emission spectra (Zhou et al., 1986). The transition involved in this emission is, for example, from a C1 donor to an acceptor complex that is composed of a Zn vacancy and a CI interstitial (Koda and Shionoya, 1964; Era et al., 1968). While the term “self-activated emission” is also used for the blue-green emission of the ZnO phosphor denoted by Z n 0 : Z n (P15),details of this emission process are not yet known. It should be noted that if all the D-A pairs have an equal pair distance, the emission spectrum does not show the time-dependent and excitationdependent spectrum regarded as characteristic of the D-A pair emission. The red emission of ZnS:Cu (Kukimoto et al., 1968) and the red emission of ZnS:Cu, In (Suzuki and Shionoya, 1971) have been ascribed to such D-A pair complexes, with the transition being considered a localized one as indicated by (e) in Fig. 1.

5. Rare-Earth and M n 2 + Ion Activators Since the improvement of the red color reproduction in color TV tubes by use of europium (Eu) activated phosphors (Levine and Palilla, 1964), not only Eu but other rare-earth elements, e.g. Ce and Tb, have become widely used as activators in phosphors. Unfortunately, rare-earth ions are not easily accommodated in ZnS, a very good host material of CRT phosphors (Langer and Ibuki, 1965), probably on account of the differences in charge and size between the rare-earth and Zn2+ ions. Better results are obtained if oxides, double oxides, and oxysulfides of Y or La are used as hosts of rare-earth activators. The emission caused by the rare-earth-ion doping originates from an extreme of the localized transition shown by (e) in Fig. 1 occurring within the 4f shell ( f - f transition) or between the 4f and 5d shells ( f - d transition) of the trivalent or divalent ion. Since the 4f electrons are shielded by the outer 5s5p electrons from environmental effects, such as the crystal field and lattice vibration, the energy levels of the 4f electrons, and therefore the emission color of an f-f transition, are not changed much using different host materials. The emissions of, for example, Tb3+ and Eu3+ions are, respectively, green and red in many kinds of host crystals, with the spectrum being composed of sharp lines almost free from vibronic effect. Dieke (1968) has extensively studied the energy levels in the 4f” (n: the number of 4f electrons, from 1 to 13) configuration of trivalent rare earth ions

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in LaCl,. Their energy-level diagram can be used for assignment of the transitions, represented by the spectral terms and J quantum numbers, for the f - f spectra of the ions in any host crystal. The main emission lines of Tb3+ and Eu3+ ions are assigned to the transitions from '0, to ' F S ,and from 50,to 'FZ,respectively. Since an f - f transition is forbidden by nature (parity forbidden), the small radiative transition probability, being partially allowed by the crystal field of the host, produces a long decay time of several milliseconds. The small transition probability, however, does not necessarily imply a low luminescence efficiency, since the efficiency is determined by the ratio of the radiative transitions to the nonradiative ones, with the latter also being small for an emitting level off-f transitions because of the shielding effect of the outer electrons. The emission of Ce3+ ions is due to an f - d transition occurring from the lowest crystal-field split 5d level to the 'D,,, and 'D312 4f levels. Such an f - d emission is generally represented as a transition between the configurations 4f" and 4.f"- ' 5 d . The f - d emission, in general, has a rather large spectral width in contrast to the sharp f - f lines. Also, the color of the f - d emission changes with different hosts because of the larger interaction of the 5d electron with its environment. The emission band of Ce3+ (n = 1) ions, for example, changes its color from UV in YPO, to yellow-green in Y3AI50,, hosts. The Ce3+ emission, being endowed with the large transition probability of a completely allowed electric dipole, has a very short decay time of several nanoseconds, and it is used in Ce-activated fast-decaying phosphors. The third type of electronic transition related to the optical spectra of rare earth ions in crystals, in addition to f - f and f - d transitions, is associated with a charge-transfer (CT) band that has a broad absorption spectrum. Transitions here are accompanied by the transfer of an electron from the closest anion to the rare-earth activator. While a C T band in luminescence has been observed only with Yb3+ ion in oxysulfide and phosphate hosts (Nakazawa, 1979),the excited state of CT absorption bands, which are often observed in the spectra of Sm, Eu, Tm, and Yb ions in various hosts, sometimes plays an important role in the excitation-relaxation process that occurs prior to the f - f emission. For example, in oxysulfide phosphors, the CT excited state (CTS) of Eu3+ ions forms a bypass from the higher levels, ' D , , , , 3 , to the '0, emitting level, thereby strongly accelerating the nonradiative relaxation among the excited levels prior to the radiative transition from the '0, emitting level (Struck and Fonger, 1971). Manganese, mainly in the divalent state, is an old but available activator. The color of the emission, which originates from a d - d transition, i.e. a transition within the 3d5 configuration of Mn" ions, is rather dependent on host materials, being, for example, green in Zn,SiO, and orange in ZnS and CaS. The emission spectrum, accompanied by vibronic spectra, is much

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broader than that of the f - f transition of rare-earth ions because of the larger crystal-field effect on the d-electrons. The effect of the crystal field on the energy levels of the d" configurations is given in the Tanabe-Sugano diagram (1954) that enables us to analyze the spectra of the d-d transition in crystals. Questions still left unsolved are where the ground state of the f " or d" configuration is located in the energy diagram of the host (see (e) of Fig. 1) and how the excitation is transferred to the localized 4f or 3d electrons. Resonance transfer of excitation energy from some other luminescent center to 4f or 3d electrons may be a probable answer for the latter question. Kingsley et al. (1965) showed that this occurred for the emission of Pr3+ in (Zn,Cd)S. McClure and Pedirini (1985) showed that a bound exciton closely coupled to the excited state of rare-earth ions is related to the excitation of the ions. Zimmermann and Boyn (1986) also showed that some unknown excited state is related to the excitation of the 4f" configuration of Tm3+ ions in ZnS. 6. Configuration Coordinate Model of Luminescent Centers

While an activator atom with some closest atoms plays the dominant role in producing a luminescent center, the surrounding atoms also interact with the center. The interaction may be treated as that in a single vibrator, in the same way as for diatomic molecules, with its energy given as a function of the displacements of its constituent atoms from the equilibrium positions. Instead of giving the complicated displacements of the interacting atoms in their individual coordinates, one generalized coordinate, which can represent the positions of all atoms at once, is used in a "configurational coordinate diagram." In such a diagram, energy of the center is represented as a function of this coordinate, in most cases without defining it strictly. In the configurational coordinate diagram shown in Fig. 2, the curves V, and U, represent the energies of a luminescent center in the ground state and in the excited state, respectively. Since the stable (equilibrium) configuration of the interacting atoms will be different for both states, the minima of the two curves do not correspond. By an optical excitation of the center, the system undergoes a vertical transition from the stable ground state, point 0 on V,, to point B on U,, in which the configuration of the atoms is not changed by the Franck-Condon restriction. Immediately after this electronic transition the system adapts to the new situation by changing its atomic configuration from B to the new equilibrium, A, along the curve U,, with the excess energy dissipated as heat. After some period (the lifetime of the center), the system undergoes a vertical jump, a radiative transition from A to D, emitting the energy difference between the two states as radiation. This fast electronic transition is then followed by the slower rearrangement of the atomic configuration from A to 0 along U,, with the excess energy dissipated as heat.

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U

FIG.2. Configurational Coordinate model of a luminescent center. The potential energy of a luminescent center is represented as a function of a generalized coordinate X, with the two parabolas, U8 and U,,corresponding respectively to the ground state and an excited state.

If the temperature of the system is so high that the thermal vibration of the surrounding atoms can stimulate the center from A to C along the curve U,, the center may transit, at the crossing point C of the curves U, and U,, from a vibrational state of the excited state to a different vibrational state of the ground state, subsequently being relaxed along U, to the stable state, 0, with the vibrational energy dissipated into the host lattice. Thus the nonradiative relaxation from A competes at high temperatures with the radiative transition from A to D, causing thermal quenching of the emission. The curvatures and the location of the minima of the two curves in Fig. 2 are theoretically related to the temperature dependence of the width of the emission spectrum, and the energy differences between A and C are related to the thermal quenching, while the differences between 0 and B, and between A and D, correspond to the peaks of the absorption and emission spectra, respectively. This enables us, from the measurements of the absorption and emission spectra at various temperatures, to draw the configurational coordinate curves and may lead to a more general understanding of the behavior of the luminescent center (Klick and Shulman, 1957). The more the character of the electronic state in the excited state differs from that in the ground state, the larger, in general, is the difference in electron-phonon coupling strength between the two, thereby causing a large shift in the coordinate of the two equilibrium points, A and 0 in Fig. 2. In accordance with the theory, a large shift of the equilibrium points induces a broad spectral width for the emission band. Conversely, an excited state possessing a similar electronic structure to that of the ground state keeps its equilibrium, as in the case of the f-f transition of rare-earth ions, at a coordinate close to that of the ground state in the configurational coordinate diagram, and may show a sharp emission line.

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B. Quenching of Luminescence

Four kinds of effects that reduce the luminescence efficiency of phosphors will be dealt with in this subsection. These include: (1) the presence of a “killer” or “quencher”, an impurity referred to in this manner when it reduces the intensity of luminescence, (2) an increase in temperature (thermal quenching), (3) too high a concentration of activators (concentration quenching), and (4)too high a level of excitation (brightness saturation). 1 . Action of Killers

The action of killers may be divided into two types. The first “bypassing”type killer captures free carriers in competition with luminescent centers during the diffusion process of the free carriers produced by excitation, allowing them to recombine nonradiatively. The second “resonance energy transfer” type removes the energy of a nearby luminescent center by means of a resonance energy transfer (Dexter, 1953). For the quenching action of the bypassing type to occur, free electrons and holes must be produced in the conduction and valence bands, while the resonance-type action can occur even in the case of an optical excitation that directly stimulates luminescent centers without producing free carriers. Since free electrons and free holes are necessarily generated initially in the luminescent processes of CRT phosphors, and since the free electrons have a rather large mobility in most CRT phosphors such as ZnS and Y,O,S, migration of the carriers will increase the likelihood that they will meet bypassing-type killers. In fact, CRT phosphors are very sensitive to killers. Inclusion of a few ppm of Fe in a ZnS phosphor, for example, can completely quench its luminescence. Furthermore, since some Fe impurity atoms form close pairs with Cu activators in ZnS: Cu phosphor, the resonance energy transfer in the pair also exerts a strong quenching effect on the activator (Tabei et al., 1975; Godlewski and Skowronski, 1985). Quenching action by resonance energy transfer is widely observed between a rare-earth ion and other rare-earth ions (Nakazawa and Shionoya, 1967). Atoms and molecules adsorbed at the surface of phosphor particles, as well as defects that are inherent in the neighbourhood of a crystal surface, often become killers and may, by quenching the luminescence near the surface, produce a “dead-voltage layer”. The thickness of this layer corresponds to the penetration depth that must be exceeded by the incident electrons to excite luminescence in the deeper active region. It is often observed that a phosphor with particle size smaller than 6-8 pm may be less efficient than one with larger particles, probably because of the larger surface-to-volume ratio of the smaller particle and the existence of a surface dead layer.

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In some cases a very small amount of killer is intentionally added to a phosphor with the aim of reducing the delayed luminescence or phosphorescence (see Section I1.C) that is undesirable for a specific application. The addition of several ppm of Ni to ZnS: Ag phosphors, for example, reduces by an order of magnitude the intensity ratio of phosphorescence to fluorescence, while quenching the fluorescence by only several percent. The mechanism of the dissipation of excitation energy in killers can be understood using a configurational coordinate model. If the bottom (A) of the excited state curve, Ue,in Fig. 2 is located close to the point C where the curve V, crosses the ground state curve ( U J , the system may in the excited state transfer its energy to the ground state at the point C. The system can then return to the stable ground state (point 0) along the curve U,, dissipating the entire energy as heat. The center is then no longer luminescent and becomes a quenching center. In other cases, however, killers may be radiative but emit energy in an infrared region.

2. Concentration Quenching Generally, too high a concentration of an activator itself causes quenching of the luminescence (concentration quenching). In this case the pairing or aggregation of activator atoms at high concentration may change a fraction of the activators to killers and induce the quenching effect. In the case of rare-earth activators, the migration of excitation by resonant energy transfer between the rare-eart h activators can sometimes be so efficient that it may carry the energy to a distant killer or to a quenching center existing at the surface of the crystal. Such excitation migration increased by activation may cause a concentration quenching of luminescence (Ozawa, 1978). At rather high concentration the migration of excitation may pass through lo5 atoms of rare earth activator before it is relaxed radiatively at one of them (Gandrud and Moose, 1968).

3. Thermal Quenching Generally, the intensity of luminescence decreases with temperature, and this sometimes changes the color balance of color TV screens at high current levels because of local heating of the phosphor. Thermal quenching may also cause the saturation of luminescence at the high electron-beam current levels used in high-brightness CRTs such as projection tubes (see Section II.B.4). As already described in Section II.A.6, the thermal quenching process of a luminescent center, represented by the configurational coordinate diagram of Fig. 2, follows the course A - G O along the two curves U, and Ug.Since the process A-C results from thermal stimulation, the probability of the nonradiative transition, WNR,is equal to the thermal activation probability Pa

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and is represented as: WNR

= Pa = sexp( - E/kT),

(3)

where the activation energy E is the difference of potential energy between the points A and C in Fig. 2, s is a frequency factor and k the Boltzmann constant. The temperature dependence of the luminescence efficiency q is then given, with WR being the radiative transition probability, as: = wR/(wR

+ wNR) a

(4)

Since the temperature dependence of WR and s is small, the temperature dependence of the luminescence intensity, i.e., thermal quenching, is expressed in Eq. (4) by the exponential part of Eq. (3). As described in Section II.A.5, both the ground state and the excited states of 4fnconfigurations of rare-earth ions in the configurational coordinate diagram have almost the same curvature and are located horizontally at the same position with no crossing point (such as point C in Fig. 2) between them. Therefore, the above-mentioned mechanism of thermal quenching cannot be applied to the luminescence caused by the f-f transition of rare earth ions. In this case the nonradiative relaxation between the 4f levels proceeds with the emission of multiphonons, and the rate of relaxation follows an energy-gap law,

K d O ) = B exp( - BE), where E denotes an energy gap between a 4f level and the next lower level, and p is the reciprocal of the effective phonon energy. At an elevated temperature the rate is increased in B in the above equation by the addition of “stimulated” emission of multiphonons to the spontaneous emission. However, because the effect on B is small for a large-gap ( E ) emitting level such as 4f emitting levels, the thermal quenching caused by the increased rate of multiphonon emission is small for the luminescence caused by the f-f transition of rare earth ions (Weber, 1967). In practice the luminescence level of rare-earth activated phosphors is retained at much higher temperatures than for other phosphors, sometimes even up to 500°C. 4. Brightness Saturation Associated with the recent trend toward large-screen projection displays, the electron-beam current density of projection CRTs is also being increased. An urgent need therefore exists to determine the cause of the brightness saturation, especially since the efficiency of luminescence may decrease in many cases to almost zero with an increase of excitation current density. A possible explanation for this phenomenon is the thermal quenching described above. Another explanation involves the saturation of luminescent

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centers whereby most of the centers are already in excited states, leaving an insufficient number of available centers in the ground state available to accept energy from the excited carriers (de Leeuw and 't Hooft, 1983). Still another explanation is the occurrence of the Auger effect, whereby an energetic free electron makes an inelastic collision with an excited electron captured at a luminescent center, ejecting it high into the conduction band and leaving the center de-excited. The probability of this process should increase at high excitation levels where the concentration of excited centers is high (Imanaga et ul., 1980). The true mechanism of the brightness saturation is still unclear even for the most common phosphors, i.e., ZnS:Ag and ZnS:Cu (Kuboniwa ef ul., 1980). It is also puzzling that the existence of a very small amount (1 ppm) of Pr or Tb in a Y,O,S:Eu phosphor can reduce its brightness saturation (Yamamoto and Kano, 1979).

C. Decuy Processes The decay time of luminescence of phosphors after the termination of excitation ranges from second to several tenths of a second or longer. When an afterglow of luminescence decays slowly, continuing for more than 0.1 second so that the human eye can observe it, the delayed luminescence is called phosphorescence. Such phosphorescence may be caused by excited charge carriers remaining for a while at a defect or impurity acting as a trap before they reach the luminescence centers. On the other hand, luminescence that terminates with the excitation is called fluorescence. 1 . Fluorescence und Phosphorescence

While the terms phosphorescence and fluorescence were initially defined as above probably with the intention to discriminate a long afterglow of luminescence from an emission that terminates with excitation, some workers in the field of luminescence research have used them differently (see Kroeger, 1948, and Leverentz, 1950). For example, fluorescence has been defined as denoting: ( 1 ) emissions that occur during excitation, with an implicitly assumed decay time of the order of lo-* second, a typical value for spontaneous emissions: (2) temperature-independent luminescence decays; (3) emission processes with an exponential decay law; (4) emissions related to the recombination of electrons not separated from the original ions; and ( 5 ) emissions taking place by spontaneous transitions. Phosphorescence has been defined as: ( 1 ) afterglow of luminescence persisting for more than lo-* second; (2) temperature-dependent luminescence decays; (3) emission processes with a power decay law; (4) afterglow due to recombination of electrons liberated

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from the original ions; and (5) emission processes involving intermediate states or traps. In the light of the advanced understanding of recent decades, the last definition (5) in each list seems to be, at least in the case of inorganic phosphors, most appropriate and inclusive of the concepts of the other definitions. It is recognized for inorganic crystals in general that the time elapsed between the initial creation of secondary electrons and holes by an incident electron, and the capture of the resultant thermalized carriers by either a recombination center or a trapping center, is extremely short ( < lo-' s) compared with the time scale of conventional observation techniques. The decay of luminescence following the termination of an excitation is, therefore, governed mainly by the time spent by the carriers in the luminescent centers and/or traps. Since the lifetime of luminescent centers, as far as inorganic phosphors are concerned, does not exceed 0.1 second, emissions persisting for more than that after the termination of excitation are generally caused by the presence of traps. These situations make consistent the initial phenomenological definition of phosphorescence with the last more physical definition (5) and also indicate that fluorescence may be denoted as an emission related only with luminescent centers, with the emission decay time being determined by the lifetime of the centers and being essentially dependent on the spontaneous transition probability. Since the lifetime of luminescent centers ranges from to s, emissions with a decay time from to lo-' s may involve both fluorescence and phosphorescence according to the last definitions. 2. Decuy of Fluorescence

In the absence of traps, excited charge carriers are directly captured by recombination centers and, if only one kind of luminescent center is present, the emission, denoted as fluorescence according to the last of the above definitions, decays exponentially as given in Eq. (5), with a decay time constant equal to the lifetime z of the center:

L(r) K exp( - t / z ) .

(5)

This type of decay is conventionally considered to follow first-order or monomolecular reaction kinetics. The lifetime of a luminescent center is determined by the total of the radiative (spontaneous) and nonradiative transition probabilities and given as z = (W, + WNJ1 (see Section II.B.3). When an electric dipole transition is allowed, the spontaneous emission probability W, is on the order of lo8 per second, as is the case with the f - d emission of Ce3+. Since a true electric dipole transition is forbidden for the f-f and d-d transitions of rare-earth and transition-metal ions as described in Section II.A.5, a magnetic dipole or a partially allowed electric dipole transition induced by the odd-symmetry

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components of the crystal field determines the spontaneous transition probability, and the lifetime of Tb3+,Eu3+,and Mn2+,for example, is of the order of a millisecond. The spontaneous transition probability W, is temperature-independent, and so is the decay of fluorescence unless the temperature-dependent nonradiative transition probability W,, is so much increased as to produce thermal quenching of luminescence. As described in Section II.A.4, the spectrum of D - A pair emission is composed of many lines or bands, each of which corresponds to differently separated pairs with a different decay rate as represented by Eq. ( 1 ) . Therefore, the decay of the total emission is given by the sum of Eq. ( 5 ) for all pairs and will no longer follow an exponential law. The actually observed decays of the D - A pair emission of ZnS:Cu, CI(AI) and ZnS:Ag, C1 phosphors follow a time power law, Lit) cc t-",

(6)

with an exponent n = 1.1-1.3 (Era rt al., 1968), as expected from theoretical calculations (Thomas et al., 1965).

3. Decay of' Phosphorescence If traps are present in a phosphor and the electrons captured in the traps can be thermally released again into the conduction band, the decay of luminescence, which is defined above as phosphorescence, will be prolonged by the time the electrons spend in the traps. The probability of thermal activation of an electron from a trap with depth E , to the conduction band (Fig. 3) is given by Pain Eq. (3) with E = ET. Therefore, the time for a carrier to remain in such a trap is given as tT

= Y 1exp(E,/kT).

(7)

Typical values of the time t , calculated from this equation for various trap depths E,, assuming s = lo9 sec-' and T = 18"C, are: one second for 0.5 eV,

*T LUMINEC. VALEKE E BA M M R.

FIG.3. A simple model of luminescent processes taking place in a phosphor containing traps

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one hour for 0.7 eV, and one day for 0.8 eV. The time t,, as well as the decay of phosphorescence, is strongly dependent on temperature, as expressed in Eq. (7). Assuming that traps of a single depth are present in a phosphor and that the electrons released from the traps go directly to luminescent centers without being recaptured by the traps, the decay of phosphorescence follows the exponential function of time similar to Eq. (5)with a timeconstant equal to t,. This exponential decay model is often used as a theoretical basis for the analysis of thermoluminescence glow curves (see Section II.C.4). In practice the observed decay of phosphorescence of CRT phosphors, however, rarely follows the exponential law. In most cases the decay, except for the earlier part, follows a time-power law such as that represented by Eq. (6), with values of the exponent in the range 0 < n < 2 (Jonscher and de Polignac, 1984). When account is taken of the fact that excited electrons in CRT phosphors seem to move around rather freely in the crystal (see Sections II.B.1 and IILD), the assumption made in the exponential law, that a retrapping process is absent, may not be reasonable for such phosphors. It seems, however, that no theoretical formulation has been given in generalized form for the phosphorescence decay that takes into account retrapping effects, and only in several limited cases, as described below, has there been given a definite formulation. If it is assumed that traps and emitting centers have an equal cross section for retrapping of a carrier released from a trap, the long-term decay of luminescence follows the time-power law of Eq. (6) with the exponent n = 2. This corresponds to so-called second-order or bimolecular reaction kinetics. When traps of various depths are distributed uniformly through the band gap, the decay curve is calculated by employing Eq. (7) and integrating it with respect to E,. The result follows a time-power law with the exponent n = 1 (see Curie, 1963).Likewise, it has been shown (Avouris and Morgan, 1981) that if tunneling of trapped electrons to luminescence centers is introduced with the tunneling distance distributed over a range, the decay is expected to follow a time-power law with n = 1. Very recently some new theoretical approaches have been investigated in order to explain the rather generally observed timepower-law decay, introducing an effect of the many-body interaction of traps (Jonscher and de Polignac, 1984) or a diffusion mechanism (Dissado, 1986). 4. Methods ,for Measurement of’ Trap Depth When a phosphor sample excited at low temperature by irradiation with ultraviolet light, x-rays, etc., is heated to a higher temperature, charge carriers frozen in traps are released and can recombine at luminescent centers. The emission stimulated by this process is called thermoluminescence. The curve representing the thermoluminescence intensity vs. temperature measured at a

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289

constant heating rate(fi)is referred to as a glow curve. While the probability of activation of the carrier from traps increases with temperature as represented by Pa in Eq. ( 3 ) , the population of trapped carriers decreases with elapsed time because of recombination. As a result, the intensity of the glow curve reaches its peak at a certain temperature. This temperature T, and the shape of the glow curve are used to obtain information on the trap depths. Many methods of analysis have been proposed based on the exponential decay model (see Section II.C.3) (Kivits and Hagebeuk, 1977). Among them the method of Hoogenstraaten (1958) seems to give good results, using the relation

E,fiJTi x exp( - ET/kT,). We can, therefore, obtain the trap depth E, from Eq. (8) by the measurements of T, for more than two values of heating rates ( f l ) (Avouris and Morgan, 1981). Very recently a transient method was proposed for the measurement of the trap characteristics (Nakazawa, 1984) in which the transient intensities of phosphorescence are measured at several definite values of delay times (t,) and normalized to the fluorescence intensity at t , = 0 in each cycle of a periodic excitation. Each of the normalized intensities is represented as a function of temperature, resulting in a curve similar to a thermoluminescence glow curve, showing a peak at temperature T,, related to the delay-time as

This relation can be used for obtaining the trap depth E , from the T, values observed for more than two different values of f d . This transient method, using a more readily determinable experimental parameter, t , , compared with /j, may make it possible to obtain more accurate results than the method of thermoluminescence.

111. CATHODE-RAY EXCITATION PROCESSES3

In most CRTs the phosphor screen is bombarded with electrons having energies between 7 and 30 keV. To understand the factors limiting efficiency and other characteristics of phosphors as well as the formulation of desirable phosphor compositions, it is necessary to consider how the energy of the electrons is converted to photons. This section describes the series of processes by which incident electrons ultimately deliver their energy to the luminescent centers. A review of early work in this area was given by Garlick (1966).

’ By H. Yamamoto

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A. Interaction

of Incident Electrons with the Surface of a Solid

Analogous with classical optics, electrons incident on a solid surface are reflected, scattered or absorbed by the solid. In addition, when they have sufficient kinetic energy, i.e., more than a few tens of eV, they can create a substantial number of secondary electrons within the solid. Of the secondary electrons, those that can overcome the work function escape into vacuum. This phenomenon, called “secondary emission”, can have an important effect on the resultant cathodoluminescence by causing the floating surface of an insulating phosphor to shift its potential when the number of incident primary electrons is not equal to number of secondary electrons escaping from the surface. The negative charging of a phosphor screen, by reducing its potential, may seriously reduce the light output and make the output unstable. Such charging is prevented in most modern CRTs by depositing a thin film of aluminum (penetrated by the electron beam) on the surface of the phosphor screen. However, it remains a major problem in vacuum fluorescent displays whose screens can not be aluminized because of their very low accelerating potentials. A review of the physics of the secondary emission process is given by Dekker (1957), and a review of the charging processes is given by Kazan and Knoll ( 1 968). The reflection and back-scattering of electrons from the surface is also important since it is another factor limiting the overall cathodoluminescent efficiency. Such electrons may also cause degradation of a picture by striking neighboring phosphor elements that are not bombarded by the primary beam. With these considerations in mind, the following section describes the events at a solid surface in greater detail. Three processes may result when an incident high-energy electron reaches the surface of a solid: (1) It may leave the surface after elastic scattering without energy loss; (2) it may leave after inelastic scattering with some energy loss; or (3) it may penetrate into the solid, producing a cascade of phonons and internal secondary electrons, some of which escape from the surface into the vacuum. The energy of the electrons leaving the surface is thus distributed in three energy regions, as shown in Fig. 4 corresponding to the above three processes. Electrons that have undergone elastic scattering and reversed direction are called reflected electrons, while those that leave the surface after having lost some fraction of their energy as a result of inelastic scattering are referred to as rediffused electrons. The number of rediffused electrons (region B in Fig. 4)is much smaller than the number of reflected electrons (shown by A). Electrons emitted from the surface with energies up to about 50 eV are frequently referred to as “true” secondaries. The total number of emitted electrons of all three categories per one incident electron is commonly called the “secondary yield” or “secondary emission ratio” and is denoted as 6.

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ELECTRON ENERGY (eV) FIG.4. The energy distribution of electrons emitted by silver after incidence of primary electrons with an energy of 160 eV. (After Rudberg, 1930). Sharp peak A is due to the reflected primary electrons, small peaks (B) close to peak A show inelastically reflected or rediffused electrons and a large broad peak C corresponds to secondary electrons.

For any material 6 depends on the accelerating voltage of the incident electrons, as qualitatively shown in Fig. 5. The yield, or 6, initially increases, except for very small voltages where most of the incident electrons are simply reflected (indicated by a broken line in Fig. 5). After passing through a maximum, the yield finally decreases with increasing voltage. The initial increase results from an increase in the average number of secondaries created by the higher energy of each incident electron. At still higher voltages the primary electrons penetrate more deeply into the solid, and many of the secondaries created are lost before reaching the surface, thus causing 6 to decrease. When ii < 1, the surface of a phosphor layer, which is generally insulating, becomes negatively charged. This occurs when the accelerating voltage is

w

Y, PRIMARY-ELECTRON ENERGY FIG. 5. Secondary-emission ratio 6 as a function of primary electron energy. In the energy

region near 0, reflected primary electrons are included with secondary electrons. [After Kazan and Knoll, 1968.1

292

TAKASHI HASE

et a1

v,

larger than in Fig. 5, causing the potential difference between the electron source (cathode) and the insulator phosphor surface to decrease until the at which point 6 = 1. For this reason, Kl is potential difference is reduced to called the “sticking potential”. Reported values of are fairly scattered for a single material and may change during bombardment. For ZnS, for example, ranges from 6 to 9 kV. In the case where the accelerating voltage is between r/; and the surface of a phosphor layer tends to charge positively since 6 > 1. However, it is prevented from becoming more positively charged than the nearest collector electrode; otherwise a decelerating field would result, reflecting some of the secondary electrons back to the phosphor surface. In actual cases, however, some of the surface charge may leak off because of a trace of adsorbed water or other polarizable substances or by breakdown through the layer. Vacuum fluorescent tubes, unlike conventional CRTs, are operated with accelerating potentials in the range of several tens to about a hundred volts. These accelerating potentials are generally less than 6 ,which is in the range of 50-200 V (Bruining, 1954). Unfortunately, an aluminizing technique cannot be used in such tubes to prevent negative charging, since the electron energy is too low to enable penetration of the Al film. To avoid negative charging a relatively conducting phosphor material such as ZnO :Zn is frequently used. Alternatively, a low-resistivity nonluminescent powder material such as In,O, may be mixed with an insulating phosphor powder. To calculate the true cathodoluminescent efficiency, one must exclude the energy of the reflected and rediffused electrons, which do not contribute to luminescence. The ratio of the number of these electrons to the number of incident electrons is referred to as the rediffusion or back-scattering factor and is denoted as qr here. By definition, it is the fraction (1 - qr) of the primary electrons that contributes to cathodoluminescence (see Part E of this section). The factor q,, while not depending markedly on the primary electron energy, increases with the weighted mean atomic number ( Z )of a phosphor, as given by the following empirical relation (Tomlin, 1963):

v,,

v,

v,

vl,

q r = i , l n Z - l4 ’

(10)

For ZnS, where Z = 23, this formula gives qr = 0.25, which agrees well with the value of 0.26 observed on an aluminized single crystal (Meyer, 1970). In the case of a powder layer (Meyer, 1970),however, a smaller value, 0.14, was observed, attributed to multiple scattering of electrons among the phosphor grains. Similarly, for YVO,:Eu, where Z = 16, an observed value of 0.20 is obtained for qr for a single crystal, and 0.14 for a powder. The calculated value in this case (from Eq. (10)) for a single crystal is 0.19. Unfortunately, experimental data of qr for phosphors are rarely reported except for the two phosphors mentioned above, requiring that an estimate be made using Eq. (10)).

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293

However, the value of qr may vary in accordance with the surface geometry of the phosphor layer, as indicated by Meyer’s experiment. It was also experimentally found that a powder layer with a rough surface may collect more back-scattered electrons (Kano and Uchida, 1983). B. Phenomenological Description of Electron Penetration

As outlined above, most of the primary electrons penetrate into a solid and lose energy by interacting with electrons and nuclei of the medium. Information on the attenuation of the electron beam, both in magnitude and energy, is essential in determining the optimum thicknesses of a phosphor screen, of its aluminum film, and also of the individual portions of multilayered screens used in penetration tubes. Studies by Ehrenberg and Franks (1953) of electron penetration into a solid were made by observing the cathodoluminescence of a crystal excited with a fine electron beam from the side (Fig. 6). A t relatively low accelerating voltages, the luminescent volume has a semispherical shape. At high voltages, it is confined to a narrow channel upon entering the crystal, terminating in a larger nearly spherical volume. This indicates that an electron with a lower energy has a larger probability of energy dissipation per unit penetration distance. The multiple-scattering paths of electrons in a solid can be visualized by a Monte Carlo calculation (Shimizu and Murata, 1971).As an example, results for Si are shown for different voltages in Fig. 7. Reduction of the forward beam current J , or the attenuation of the number of primary electrons with depth x in a solid, is given by the following law

Phosphor

FIG.6. Schematic illustration of luminescence envelopes within a phosphor crystal excited by an electron beam. A, B, and C correspond to increasing primary electron energy. [After Garlick 1966; based on results of Ehrenberg and Franks, 1953.1

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8.0

4.0

8.0

4.0

8.0

4.0

4.0$

8.0

4.0

0

8.O(pm)

4.0

(a110 k V

12.0

4.0

8.0

’

4.0

8.0

8.01

4.0

8.0

12.0

FIG. 7. Multiple scattering of electrons in Si calculated by Monte Carlo method (by courtesy of Mr. Suga, Central Research Laboratory, Hitachi Ltd.). The primary electrons are incident perpendicular to the surface with energies of 10 kV (a), 20 k V (b), 30 kV (c) and 50 k V (d).

(Lenard, 1918), which is similar to that for the absorption of light: J

= Jo exp( - ax),

where = b’pJE’.

Here J,, is the current density at the surface, eE is the kinetic energy of the electrons after having penetrated to the depth of x,p is the density of the solid and b‘ is a constant that is characteristic of the solid. Measurements of Terrill (1924) on the current passing through different thicknesses of aluminum films gave b’ = 8 x 10” V2cm2/g, so that a in Eq. (1 1) becomes 2.2 x 10l2 cm-’. On theoretical grounds the energy dissipation of an electron in a solid is

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295

given by Bethe’s formula (Bethe, 1930): -

d ~ / l i . \ .= ( 2 7 c ~ ~ e 1n(E/E,), 4/~)

(12)

where E is the kinetic energy of the primary electron at depth x, N is the number density of all the electrons in the solid. Z is the mean atomic number of the material and E , is the averaged ionization energies of all the electrons of the constituent atoms. As indicated by the formula, the specific energy loss, -dE/dx, increases with a decrease in E , in agreement with the qualitative results shown in Fig. 6. The relationship between the energy of an electron and depth of penetration x is most frequently expressed by the empirically obtained Thomson- Whiddington law (Whiddington, 1912), which can be derived as an approximation from Eq. ( 1 2): E

=

E, { 1

-

( x / R ) }l ” .

(13)

Here E , is the energy of a primary electron and R is a constant characteristic of the material. As evident from Eq. (13), at a depth x = R the energy falls to zero. This depth is referred to as the “range” of the electrons. It is of interest to note that - d E / d x increases monotonically with x according to Eq. ( 1 3). For E , = 1 to 10 kV, R is given as a function of material parameters by the following empirical relation (Feldman, 1960): R

=

25(A/p)(E0/Z”’)“

= bE:

(14)

with n = 1.2/( I

-

0.29 log,, Z )

(15)

Here p is the bulk density. A the molecular weight and Z the atomic number or the number of electrons per molecule of the material. If the energy E , is given in keV, R is obtained in nm (10 A). Experimental values of n and b are given for ZnS, CdS, CdWO,, Zn,SiO,, Al, etc., in the paper by Feldman ( 1960). We can estimate R for any material by Eqs. ( 1 3) and (14). In the case of the aluminum film on the back of the phosphor screen, which is usually as thick as 200 nm, the minimum anode voltage required for electrons to get through this film is estimated to be 3 kV. For ZnO excited by 1 kV electrons, R is only 6 nm, indicating that low-energy electrons employed in the vacuum fluorescent displays excite only the surface layer of the phosphor. For the electron range in ZnS, Kingsley and Prener (1972) give the following empirical formula, which can be applied at least up to 20 kV: R’(E,) = 1 1.6Ehh5

(in nm).

(16)

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TAKASHI HASE et al

t

w

tr 3 VOLTAGE ( k V )

FIG. 8. Cathodoluminescence intensity of ZnS:Ag, C1 as a function of the primary electron energy. The dead voltage is denoted as V,. [Reprinted with permission from J . Phys. Solids 17, Gergley, G., “Surface recombination and diffusion processes in cathodoluminescence and electron bombardmentinduced conductivity.” Copyright 1960, Pergamon Press PLC.]

This formula was derived by making use of Makhov’s formula (1960) that gives the beam power dissipated in a solid. The range R‘ here is defined as the depth where the beam power is exp( -2) times the initial value. At E , = 20 kV, Eq. (16) gives R’ = 1.6pm, a fairly small value compared to the average particle size of commercial ZnS phosphors, which is about 8 to 10 pm. When E , is decreased (assuming the beam current to be maintained) the cathodoluminescence is found to fall essentially to zero below a certain threshold voltage. For powder phosphor screens the threshold usually ranges from lo2 V to a few kV, depending on the material and its preparation. Well above the threshold, the luminescent intensity has a nearly linear dependence on E,. Typical of this is the case of ZnS:Ag, CI shown in Fig. 8 (Gergely, 1960). However, at sufficiently high values of E,, the luminescence may increase at a rate less than linear if the beam penetrates the phosphor to the substrate. The intercept of the straight-line portion of the curve with the abscissa is called the “dead voltage”. The existence of the dead voltage is often ascribed to the nonradiative surface recombination of the carriers. The dead voltage, however, may be as low as 2.2 V in some low-resistance materials such as Zn0:Zn. Even the simple mixing of the usual high-resistance phosphor powder with a lowresistance nonluminescent material can decrease the effective dead voltage to several hundred volts, suggesting that surface charging is an important

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297

3 ELECTRON ENERGY (eV)

FIG.9. Quantum yield and power efficiency of cathodoluminescence (lower) from a clean surface of a CdS crystal at 80 K as a function of the electron energy O n the surface, cleaved in vacuum. some cathode material (presumably Ba) that has a low work-function was evaporated. Light was observed at a wavelength of 523 nm. [After Steinrisser, 1970.1

factor in determining the dead voltage. Luminescence at a few volts has also been reported from a clean surface of CdS on which a low-work-function material has been evaporated (Fig. 9; Steinrisser, 1970). It should be noted that the range in this case is less than 1 nm at 70 volts. C. Elrrnentary Procrsses Resulting] jrom Cathode-Ray Excitation

The elementary processes of electron energy dissipation can be directly observed by the technique of characteristic energy loss spectroscopy. The loss spectrum of YVO, shown in Fig. 10 was obtained by energy analysis of an electron that had passed through a thin edge of a microcrystal (Tonomura et d.,1978). In principle, the same information can be obtained by analysis of the energy of the rediffused electrons. The dominant peaks in Fig. 10 are assigned to a plasmon excitation (peak B) and core electron excitation (peaks C and D). An interband transition inside a VOi- group is also seen weakly (peak A). Beyond the energy region shown in Fig. 10 ( > 8 0 eV) any energy losses have not been identified for YVO,, ZnS and other typical phosphor materials. Although this is a good example demonstrating what kinds of processes are possible, many materials show simpler spectra. Core electron excitation can be found in materials containing an element with a large atomic

298

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ELECTRON ENERGY ( e v ) FIG. 10. Electron energy loss spectrum of YVO,. For assignment of peaks, see text. [After Tonomura et a/., 1978.1

number, e.g. rare-earth compounds, while a plasmon excitation peak is strong in any material and is the only dominant one in materials that do not have an element with a large atomic number. A plasmon in insulators is created by valence electrons oscillating in phase. It decays within seconds and is converted to excitation of a single electron with an energy much higher than the band gap (Pines, 1956). Thus, a high-energy primary electron in a solid can generate secondary carriers (electrons and holes) having energies of several tens of eV. Each of these secondary electrons or holes in turn creates a phonon and another pair of carriers with lower energy each time it is scattered by ions. This avalanching process goes on until the energy of the carriers becomes lower than the ionization threshold. The final products of the entire process are electrons and holes near the band edges (thermalized carriers) and phonons. Such ionization processes are schematically illustrated in Fig. 1 1 (Robbins, 1980).

D. Host Sensitization The next step leading to cathodoluminescence involves the migration and radiative recombination of electron-hole pairs. This process is similar to the photoluminescent process occurring under band-gap energy excitation. Photoluminescence often occurs by irradiation with light whose wavelength corresponds to the absorption of the host lattice. This is evidence of energy transfer from the host to activators, often called “host sensitization”. In materials exhibiting photoconductivity, the energy is transfered from the host lattice to activators by the transport of electrons and holes. Representative of such materials are commercial TV phosphors, ZnS:Cu, Al

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primary

hJ&:f

0

a w

,,

optical phonon losses

\

\ ionization threshold ther m a Ii z a tion

FIG. 11. Schematic illustration of ionization processes in a solid by an incident high-energy electron. Longitudinal optical phonons with an energy hv,,, are generated, as well as secondary electrons and holes, until the electron energy decreases below the threshold. [After Robbins, 1980. Reprinted by permission of the publisher, The Electrochemical Society, Inc.]

(green) and ZnS:Ag, CI (blue). In these materials, donors (A1 or C1) may capture transported electrons while acceptors (Cu or Ag) may capture holes as a result of the potentials associated with the excess charges. Captured electrons and holes may then recombine at a donor-acceptor pair, with the released energy appearing as the luminescence characteristic of the pair (see Section II.A.5). In other cases the undoped host material may have its own luminescent centers composed of atom vacancies or localized atomic groups (molecular complexes). The energy can then be transferred from such “host luminescent centers” to doped activators via resonance energy transfer instead of by the carrier transport mechanism. (The resonance energy transfer may be pictured by means of its analogy with sound resonance between two identical tuning forks.) The energy can be transferred from the donor to the acceptor without actually emitting light if there is a good energy match between the two. A typical example is YV0,:Eu3+ (Palilla et al., 1965), where the energy is transferred from a V0:- ion to Eu3+.This process also occurs in compounds with complex ions such as WOi-, MOO:- and NbOi-. These materials, e g , CaWO,, SrMoO,, Y N b 0 , and YVO,, exhibit a significant amount of luminescence that originates in the complex ions when no activator ions are present. The complex ions in this case are excited to unoccupied molecular orbital states by interaction with secondary electrons. In addition, a small part of the primary electrons can directly excite the ions, as shown in Fig. 10. Such resonance energy transfer has also been found in ZnS and CdS activated with a rare earth ion, in which case residual Ib-group impurities play the role of the host luminescent centers (Kingsley et al., 1965).

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In materials that show only faint host luminescence, the situation is less obvious. Recent studies, however, have provided many indications that the appearance of activator luminescence is preceded by some degree of carrier or exciton localization near the activator ions. A comprehensive review on this subject was given by Robbins and Dean (1978). The activators that have net charges can also bind carriers in the form of excitons by the long-range Coulomb potential that they generate. For example, the excitation spectrum of SnO,: Eu3' shows intrinsic exciton lines at 4.2 K (Manabe, 1980). On the other hand, isoelectronic centers, which have no net charge, can form bound states by a short-range central cell potential. Thomas (1966) showed that the principal factors affecting the binding potential are, first, the electronegativity difference between the impurity and the host ion for which it substitutes and, second, lattice distortion induced by the substitution. Isoelectronic impurities in semiconductors, the understanding of which has been clarified on the basis of this idea, are mostly anions: e.g., N in G a P or 0 in ZnTe. This model helps to make clear the energy capture process of cation impurities as well. The binding potential in this case originates from a difference in ionization potential, even when chemical electronegativities d o not vary greatly as in rare-earth elements. When a rare-earth element substituting for yttrium (a typical element that constitutes the host crystal of rare-earth phosphors) has a third ionization potential substantially lower than that of Y (yttrium), it will have a larger electron affinity than Y. Meanwhile, an element with a smaller fourth ionization potential will attract a hole. Expressed in terms of chemistry, a trivalent ion easily reducible to a divalent state attracts an electron, while an ion that tends to be oxidized The former class is represented by Eu3+, collects a hole when it replaces Y Yb3' and Sm3+, and the latter by Ce3+, Tb3+ and Pr3+. After the ion binds an electron or a hole, it further attracts an alternate carrier (i.e., a hole or an electron), forming an exciton around the ion. When the electron and hole recombine, the released energy is instantaneously used to excite a 4f electron from its ground state to an excited state. In rare-earth-activated Y,O,S, the two types of ions show thermoluminescent glow peaks different from each other, indicating a difference in the species of carriers they first trap. For rare-earth-activated Y 2 0 2 S and Y,AI,O,, ,a positive correlation is found between relative quantum yields and ionization potentials of rare-earth elements. An exception is Ce'' in Y20,S, which does not emit at room temperature. The second class of ions, Ce3+, Tb3+ and Pr3+ in Y 2 0 3 , does not have high efficiencies, probably because each of these ions is partly in the tetravalent state. In fact, Y,O, doped with these ions at a concentration level of 1% or higher is colored because of strong absorption of a mixed valence state.

'+.

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0

30 1

valence band

I I

Fic;. 12. A schematic model of the charge transfer state (CTS) of Eu3+. In CTS a hole is bound in a potential well due to theeffective negative charge of Eu” and migrates on p-orbitals of anions ( I ) , while it is tightly bound to E u ” , the resultant state being Eu” (2). Polarization of anions is also shown. [After Hoshina, 1977.1

When an electron is transferred from a ligand ion to Eu3+,leaving a hole at the ligand, Eu3+ is in its charge transfer state (CTS).The hole can then migrate among equivalent ligand ions, while the electron is accommodated in a localized 4f orbital. This situation, illustrated in Fig. 12 (Hoshina et al., 1977) represents an exciton-binding state of the first class of ions, Eu3+,Sm3+ and Yb3+.If the CTS is located at an energy lower than the band gap, Eu3+ can bind an exciton and produce efficient luminescence. In contrast to the com: Eu, isostructural I n 2 0 3 :Eu has poor efficiency at mercial phosphor Y 203 room temperature4. This difference can be related to an observation that the

This is not the case under low-energy electron excitation, where In,O,:Eu shows luminescence by virtue of its low resistivity, which prevents charge buildup, while Y,O,: Eu does not.

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0

200 250 300 350 WAVELENGTH ( n m ) FIG. 13. Differential diffuse reflectance spectra of (Y,In),0,:Eu3+. The percentages indicate In content. [After Yamamoto and Urdbe, 1982. Reprinted by permission of the publisher, The Electrochemical Society, Inc.]

intensity of the CTS band decreases with In content of the solid solution (Y, In),O, : Eu (Fig. 13;Yamamoto and Urabe, 1982).The decrease in the CTS band intensity is caused by the fact that In has a smaller third ionization potential than Y. The ions Ce3+, Pr3+ and Tb3+ have the same type of electronic configuration, 4fn-'5d, when they are in the emitting state (the ground state is 4f" with n being 1, 3 and 8).In this state, a hole is left inside 4f orbitals, and an electron is liberated to a less localized 5d orbital. Therefore, in a way analogous to CTS, this is another exciton-binding state. Figure 14 (Jplrgensen, 1962) shows the energies of the CTS and 4fn-'5d states plotted against the number of 4f electrons in trivalent rare earth ions. Again it should be emphasized that the ions having either a CTS or 4fn--'5d state at low energies can capture excitation energy and, as a consequence, emit efficiently. In addition, these states at low energies have important effects on the luminescent properties. Struck and Fonger (1971)proposed a model in which the CTS of Eu3+ is thermally decomposed into Eu2+ and a free hole. Hoshina et al. (1977)have pointed out that the Eu3+ CTS induces spectral changes of 4f intraconfigurational transitions through mixing with the ground state, 4f6. Some evidence of exciton binding at an isoelectronic cation impurity was reported by Kawai and Hoshina (1979),who found exciton lines in the excitation spectrum of ZnS: MnZ+.Since Mn has a smaller second ionization energy than Zn, Mn2+ presumably captures a hole first.

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80 V

f = l 2 3 4 5 6 7 8 9 1011 1213 Ce Nd Sm Gd Dy Er Yb Pr Pm Eu Tb Ho Tm

NUMBER OF 4f ELECTRONS FIG. 14. The energies of CTS and 4/’”-’5d states as a function of the number of 4f electrons in trivalent rare-earth ions. [After Jflrgensen et d., 1962.1

The diffusion length of a free carrier is one of the important factors in the transport of excitation energy and, in turn, the efficiency or the optimum activator concentration. In the case of GaAs or (Ga, AI)As, a slight scratch on a wafer caused by tweezers is observed to quench the luminescence of the whole wafer. This is caused by nonradiative recombination of carriers reaching the scratch and demonstrates why semiconductors with high carrier mobilities (or diffusion lengths) cannot be good phosphor hosts. On the other hand, a material with a short diffusion length suffers, because an activator can capture carriers only in its vicinity. An optimum diffusion length is thus expected, which probably falls around that of the most efficient host materials, ZnS or CdS. Specific values of the diffusion lengths are not known, but they probably range from a hundred or several tens of atomic distances for ZnS to a few atomic distances for oxides with a large band gap. The oxides require a high concentration of activators to compensate for the short diffusion lengths and are also relatively insensitive to quenching impurities. E . Cathodoluminrscence Efficiency

The energy efficiency of cathodoluminescence is usually expressed as a product of the efficiencies of the elementary processes described above. Here, in accordance with the recent work of Inoue (1984) and Robbins (1980), we write the overall efficiency, v ] , as follows: v] = ( 1 -

vl,)I;hv,&

(17)

304

TAKASHI HASE rt al.

where q, is the rediffusion or back-scattering factor (the fraction of energy of rediffused or back-scattered electrons to the primary energy), vp is the average frequency of the emitted photons, S is the efficiency of the radiative recombination excited by thermalized pairs, and I; is the “limiting quantum yield” of the pair creation defined as the ratio of the quantum yield n ( E ) to the energy E of the primary electron:

I; = ( n ( E ) ) / E .

(18)

According to this definition. I; is the inverse of the average energy 4: dissipated in creating an electron-hole pair; 5 = Y;’. Studies on semiconductor radiation detectors have provided an empirical relationship 5 = PE,, where the coefficient fl is given as follows (Klein, 1968): /j’ =

2.67E,

+ 0.87

(eV),

(19)

or, approximately, fl = 3.5,. Van Roosbroek (1965) used a statistical model to calculate I;.This model is equivalent to a problem of cutting boards in a random way, simulating division of the electron energy into the two competing processes: pair creation, and loss by phonon emission. The ratio of the rate of phonon emission loss to the rate of pair creation (the branching ratio) is assumed to be a constant independent of the electron energy. However, this is not actually the case. The loss by optical phonon emission increases as the electron energy decreases and competes with the ionization scattering in the energy range a few times the size of the ionization threshold. The model is based on many simplifications in addition to this, but Robbins (1980) found that the model works in predicting maximum efficiencies of typical phosphors in reasonable agreement with observed efficiencies. Inoue (1984) refined this approach by evaluating the energy-dependent loss parameter in terms of material constants using simple models for electron-phonon and electron-electron interactions. For binary compounds having the chemical formula A,B,.,, the effects of the material constants can be summarized as follows. (1) The theoretical value of fl = ( / E , is about 3.5 for crystal lattices consisting of group-IV elements, and decreases to 2.1 towards 11-VI compounds. It lies close to 2 also for I-VII compounds having the rock salt or cesium chloride structure. (2) It is empirically known that a large valence electron density (n,) is correlated with a low cathodoluminescent efficiency. The theory shows that the ionization scattering rate is proportionate to n;713. Equivalently, a small lattice constant increases the phonon emission loss drastically. (3) The phonon emission loss through the deformation potential is

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES

305

proportional to the square of the covalency. In this respect it may be concluded that 11-VI compounds are characterized by a smaller phonon loss than group-VI elements and 111-V compounds with the same lattice constant. (4) The loss parameter associated with the long-range electrostatic potential (S,) is related to the frequency of the longitudinal optical phonon cotOand the effective dielectric constant E* as S,

= (constant) x o&/E*

On the other hand, the loss parameter due to the deformation potential S, is relatively insensitive to the phonon frequency. It is empirically known that materials having a high IR active optical phonon frequency do not show high luminescence efficiencies. This fact may indicate that the phonon emission loss is dominated by the long-range electrostatic interaction in these materials. The effective dielectric constant decreases from 111-V towards I- VII compounds, enhancing the electrostatic interaction in the ionic materials. High-frequency phonons can also cause nonradiative relaxation in an activator, thus decreasing S in Eq. ( 1 7). Materials having atom groups oscillating at high frequencies are poor phosphors. Examples of these groups are O H - , CO5- and SO:-. Observed values of r] and some material parameters characterizing it are given in Table I. Absolute measurements of efficiency have been carried out TABLE I PARAMETERS' CHARACTERIZING EFFICIENCIES OF CATHODE-RAY-EXCITED PHOSPHORS. '1 = ( 1

ZnS:Ag, CI ZnS:Cu CaS :Ce ZnO : Zn CaO: Pb NaI:TI Y,O,:Eu

Y,02S:Eu

3.87 3.87 4.4d 3.35 7.7 5.9 5.6 4.6

-

2.82 2.3 2.3 2.4 3.45 3.27 2 2

'lb)(pEB)-'hVpS

2.12 2.12 2.03 2.65 2.04 2.02 (3)' (3)'

" See text for definition of the parameters. Otherwise stated, cited from lnoue (1984). Calculated with qb = 0.1 and S = 0.9. Indirect band gap (Kaneko, 1984). ' Assumed on the basis of Klein's work (1968).

0.28 0.23 0.21 0.22 0.18 0.22 0.10 0.12

0.21 0.17-0.23 0.22 0.07 0.10

0.13 0.087 0.10-0.13

306

TAKASHI HASE et al.

only on a small number of phosphors such as ZnS:Ag, C1. The efficiency of many other phosphors has been determined by comparing them with these measured materials. The back-scattering factor is taken to be 0.1 for all the materials. It should be noted that commercial TV phosphors, ZnS: Ag, CI, ZnS:Cu, A1 and Y,O,S:Eu, show a value of p that is close to the ultimate

t

t; m 0

z

5:0. 5

3

-< w W

I-

J

W

a 01 0

I

I

0.5 1 .o CURRENT DENSITY (amperelcd)

FIG. 15. The relative luminosity of typical green-emitting phosphors as a function of current density (Meyer and Palilla, 1969). The unit of the abscissa is given in A/cmz instantaneous current A/cmz averaged over time in this experiment. (a) (Zn, Cd)S: density, which is equivalent to 6 x Ag, (b)Zn,SiO,: Mn, (c) Y,SiO,: Tb, (d) InBO,: Tb and (e) YPO,: Tb. [Reprinted by permission of the publisher, The Electrochemical Society, Inc.]

a

z

@ 4 u

'oor77T=F 80

/

/' I

I

100

1

I

200

I

I

300

I

I

400

TEMPERATURE ( O C 1 FIG.16. The luminous efficiency as a function of temperature for several commonly used CRT phosphors (Kazan, 1985). (a) ZnS:Ag, (b) ZnS:Cu, (c) Zn,SiO,:Mn and (d) Y,O,:Eu.

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES

307

value of about 3. For materials with polyanion complexes it is difficult to define E,, since the fundamental absorption edge has its origin in a localized transition inside the complex. Generally speaking, the efficiency depends on the excitation density and temperature. Degradation of the efficiency with an increase in the current density is called “brightness saturation” (see Section 11.B.4),and degradation with temperature is called “thermal quenching” (see Section II.B.3). To give an idea of how much degradation can occur, the efficiency or the brightness is shown as a function of current density (Meyer and Palilla, 1969) and temperature (Kazan, 1985) respectively in Figs. 15 and 16.

Iv.

PHOSPHOR

MATERIALS FOR

SPECIFIC

APPLICATIONS

A . Television

As is well known, additive mixing of primary colors in the form of blue, green and red phosphor emissions allows production of colors within the triangle shown in the chromaticity diagram (Fig. 17). When the dots or stripes of a particular color phosphor are excited in an actual tube, the color coordinates obtained are shifted more or less from those expected for the phosphor towards the center of the chromaticity diagram. This color shift is primarily due to the the addition of light emission from phosphor elements of other color excited by the elastically scattered electrons from the holes of the shadow mask. Also, there may be a cross-contamination of a particular phosphor with phosphors of other colors during the screening process. Typical phosphors for color TV are shown in Appendix 1. The emission color of the green primary has been chosen as a compromise between obtaining a larger area of color reproduction in the chromaticity diagram and more equal electron beam currents for exciting the three color phosphors to produce reference white. In this connection, efforts have been made to shift the emission peak of 530 nm of green-emitting ZnS: Cu, C1 (or Al) to a longer wavelength (530-560 nm) either by employing a solid solution Zn, -.Cd,S or by introducing a deeper acceptor such as Au. The latter has been preferred in Japan in order to avoid Cd pollution. These efforts have brought the ratio of the currents in the three guns closer to unity for producing white light and increased the white brightness/(total current) at the sacrifice of the color gamut of the system. This sacrifice was considered relatively unimportant, since few colors occurring in nature (or in artificial

’ By T. Kano

308

TAKASHI HASE et al.

r 0.91

N TSC

0.8 I-/ 0.7

0.4

0.3

I Lo

0

0.2

J

FIG. 17. Color coordinates of NTSC standard, typical primary phosphors and a typical color picture tube (CPT).The color region reproduced by the color picture tube is smaller than the region spanned by the three primary phosphors because of phosphor cross-contamination and scattering of the electron beam. The small circles at the center represent white colors used as working standards for describing performance of CPTs.

dyes or pigments) are found outside the resulting color gamut that can be reproduced. However, a test on observers at Hitachi Ltd. (unpublished) showed that color pictures generated using Zn,SiO,: Mn2+ as the green primary were strongly favored by Japanese individuals. Although the emission of Zn,Si04:Mn2+ has color coordinates close to the NTSC green, it has not found much practical use because of its relatively long persistence (about 25 ms) as well as its low energy efficiency of emission (about 8%). Thus, a significant improvement could be realized if a more efficient phosphor were developed having the green emission color of Zn,Si0,:Mn2+ but with less persistence. For the blue primary, ZnS: Ag has been continuously employed in contrast with the shift in the choice of the green phosphors. Its reported energy efficiency (21-25%) is the highest of all phosphors and has been estimated to be nearly at the theoretical limit (Garlick, 1966). Its emission spectrum is also satisfactory compared to other blue primaries. For the red primary, the broad band emissions of Zn,(PO,),: Mn2+ and

P H O S P H O R MATERIALS F O R CATHODE-RAY T U B E S

309

(Zn, Cd)S:Ag were employed in the early stages of color TV. As early as 1955, it was recognized that a good red primary should have a narrow emission band around 610 nm and an especially sharp cutoff towards the shorter wavelengths (Bril and Klasens, 1955). Somewhat dramatically, this requirement was actually met first by YV0,:Eu3+ (Levine and Palilla, 1964) and later by Y 2 0 3 : E u 3 +as well as by Y202S:Eu3+(Royce and Smith, 1968). The latter two phosphors have superseded the former because of their higher brightness. The emission spectra of (Zn, Cd)S:Ag, Y202S:Eu3+and Y2W30,,:Eu3+ are compared in Fig. 18. The spectra of the other red-emitting phosphors are given in Appendix 1. The red-emitting Eu3+ ion is a member of the lanthanides (elements having atomic numbers from 57 (La) to 71 (Lu) whose chemical properties have long been known to be very similar). As the host constituent, the Y 3 + ion (atomic number 39) has similar chemical properties. The lanthanides and yttrium (sometimes including scandium) are grouped together as "rare earths". The separation of these rare-earth elements, which had been a major objective of inorganic chemistry, was greatly advanced industrially in the middle of the 1960s by the demand for a supply of highly pure Y 2 0 3 and E u 2 0 3as the raw materials of red phosphors for color TV. (Gshneidner and Eyring, 1979- 1986; Kano and Yanagida, 1980). Assuming a spectral emission curve with a Gaussian shape, giving NTSC red (x:0.67, y:0.33), the luminous efficiency would decrease with an increase in half-width because of the rapid decrease of visual sensitivity in the longerwavelength region (Kano p r ul., 1982).Thanks to their high lumen equivalents, the brightness of narrow-band Eu3+-activated phosphors is thus higher than that of the broad-band phosphors even when their energy efficiencies are lower. The relative brightness of red phosphors is compared in terms of their luminous and energy efficiency in Table 11. As is commonly the case for emission due to transitions within the 41' orbital, the emission spectrum of Eu3+ is relatively insensitive to the host materials. Nevertheless, the variation in the Eu3+emission spectrum with host material is still significant. The emission spectrum of Y 2 0 2 S : E u 3 +consists of a main line at 626 nm and sublines around 590 nm and 710 nm. Because of the relatively intense sublines, the L value of the emission, defined as the lumen equivalent relative to monochromatic light having the same x value, is only 55?,, (at 3.5 mol I{', Eu). The sublines around 590 nm cause the red color of the main line to shift to the yellow side, narrowing the chromaticity area that is reproducible by the three primaries. Their emitting state is 'D,, while the main line (626 nm) is due to 5D0. With increase in Eu3+concentration, the emission from 'D1 decreases more rapidly than that from 'Do, because of the crossrelaxation between ( 5D1-5D0) and ( 7F0-7F3). In effect, the yellow-emitting %, state relaxes, without radiation, to 'Do, transferring energy to the nearest

310

WAVELENGTH (nm 1 FIG.18. Emission spectra of red phosphors: (a) (Zn,Cd)S:Ag, (b) Y20,S:Eu3+ (with 3.5 mol. Eu and pigmented) and (c) Y 2 W , 0 , , : E u 3 + . A high lumen equivalent value of Y,W3OI2:Eu3+was reported by Kano ef nl. (1982). See also Table I1 for comparison with other red phosphors.

Eu3' (ground state 'FO). Because of the more efficient cross-relaxation between Eu3'( 'D,)and Sm3' (ground state %,,*), partial substitution of expensive Eu3+ by Sm3+-for example, 2.7 mol % Eu3 + 0.1 mol % Sm3+ instead of 2.9 mol Eu3+-contributes to a reduction in the cost of raw materials without changing the emission color of the phosphor (Yamamoto el al., 1977). Among many red phosphors so far investigated, Y,W,OI2:Eu3+ has the encouraging further exploratory research to obtain highest L value (8 1 even brighter red Eu3+ phosphors (Kano ct al., 1982).

x,),

31 1

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES TABLE 11 LUMINESCENT PROPERTIES OF RED PHOSPHORS FOR COLORTV ~~

Color coordinates

energy efficiency

Phosphor

Y

J’

I m/’W

L“

(%)

Zn,(P0,)2:Mn (Zn, Cd)S:Ag YV0,:Eu Y,O,:Eu Y,02S:Eu Y2W,O,z :Eu 61 1 nm light

0.665 0.665 0.664 0.640 0.648 0.656 0.669

0.335 0.336 0.330 0.352 0.344 0.342 0.331

I63

47 2s 62 70 5s ni 100

6.7 16.0 7.1

nn

21 7 284 21s 300 33s

Relative brightness

13.0 4.3

39 51 55 88 100 46

-

-

8.7

L : Lumen equivalent relative to monochromatic light of wavelength 61 I nm.

At present, almost all manufacturers of color CRTs prefer Y20,S: Eu3+ to Y,O,:Eu”+, since the former is so acid-resistant that one can recover it from previously screened suspensions contaminated with blue and green ZnS phosphors by dissolving the latter in an acid. In pure Y,O,S: Eu3+, the brightness saturates with an increase in excitation power density. This characteristic was often masked by a trace amount (about 10 ppm) of T b 3 + ,which was found to prevent the saturation (Yamamoto and Kano, 1979). At present, a trace amount of Tb (or Pr) is thus intentionally added to the Y,O, raw material used for preparing Y 202 S : Eu It is difficult at present to maintain a pure white color at high brightness, since the efficiencies of the green and blue ZnS phosphors are reduced, while that of the red Eu3+ phosphor remains relatively constant with increase in current density. To minimize this problem, a mixture of a linear-responding green phosphor, Y2O,S:Tb3’, with a green ZnS:Cu, Au, A1 phosphor was tried, showing a significant improvement (Itoh et al., 1981). Although the emission colors of Tb3+-activatedphosphors are not ideal and their material cost is high, it is expected that more attention will be given to the linear green Tb’+-activated phosphors when more sharply focused electron beams with higher current density become available. The brightness saturation of the blue ZnS phosphor also creates a problem similar to that occurring with the green ZnS. For such high-current-density applications, the linear response of Sr,(P04),CI: Eu2+ blue phosphor with current density was investigated (Meyer and Palilla, 1969). Unfortunately its efficiency level is insufficient to attract much attention and in contrast with Eu 3 t or Tb3+-activated phosphors, the emission color of Eu” phosphors is

’+.

312

TAKASHI HASE et al.

strongly dependent on the host material, making research on blue Eu2+activated phosphor more difficult. Since efforts are being directed toward obtaining electron beams with smaller spot size by means of improved cathodes and electron-lens systems, advances in these areas will create a greater demand for linear green and blue phosphors in the future.

B. Terminal Displays6

Phosphors employed in most CRT terminal displays are frequently the same as those used for color TV. However, longer-persistence phosphors not suited for TV may be employed, since terminal displays are usually used for generating characters or graphics where movement is not so rapid as in TV. Phosphors now in use for monochrome CRT terminal displays are ZnS:Cu, CI for green and Cd,(P04)3CI:Mn2+ or InB03:Tb3+, Eu3+ for orange (Yamamoto, Megumi et al., 1989). For white, usually a mixture of two or more phosphors is used, such as InB03:Eu3++ InB0,:Tb3+; InBO3:Eu3+ + Zn2Si04:Mn2+;InB03:Eu3+,Tb3+ and (Zn,Cd)S:Cu, Al, G a + ZnS :Ag, Ga, C1. Frequently, dark characters are produced on a white background to simulate printed matter. However, when a mixture of phosphors is used, color effects may be produced because of differences in aging, saturation with beam current or differences in decay time of the constituents. A white-emitting phosphor consisting of a single component is thus desired to avoid such color inhomogeneities. To display high-definition figures such as Chinese characters, or smooth diagonal lines that do not appear jagged, a large number of scan lines is required. In this case, to avoid the need for increasing the frequncy range of the electronic circuits, lower frame frequencies are used. However, to avoid or minimize the resultant flicker, long-persistence phosphors are used (Zn2Si0,:Mn2+ for green, Zn3(P04),:Mn2+for red and ZnS:Ag, Ga, CI for blue, as indicated in Appendix 1). The persistence of the green emission of Zn2Si04:Mn2+,As (P39) The green phosphor is about 150 ms (time for brightness to decay to emission is due to the transition in the 3d electronic orbital of Mn2+ions. The decay time of this transition is 25 ms as is observed on Zn,SiO,: Mn2+.If As is added as a dopant, longer persistence is obtained by trapping excited electrons (Chang and Sai-Halasz, 1980). These trapped electrons are released from the

A).

' By T. Kano

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES

313

traps by thermal stimulation after about 150 ms and radiatively recombine with holes, which are assumed to be trapped at the Mn ions. The emission peak of Zn,SiO,: M n Z + As , is 525 nm, which is identical to that of Zn,Si0,:Mn2+. The above longer-persistence phosphors are, however, only about half as bright as T V phosphors of the corresponding color. Because of this, their use is restricted even in computer-terminal applications. Also, the potential of burning in these phosphors has been occasionally noted by a residual darkening or decreased brightness in phosphor areas scanned for a long time (see Section VIII). C. Color Projection Displays'

To produce a large color picture, images from three small CRTs emitting blue, green and red light, respectively, are optically projected and superimposed on the projection screen to form a composite picture in full color. The phosphors used for this purpose are excited at current densities (averaged over the screen area) of up to about 30 pA/cm2, one order of magnitude higher than those in direct-viewing CRTs. Typical phosphors for projection CRTs are listed in Appendix 1. The first criterion in choosing phosphors for projection CRTs is the linearity of the brightness with respect to the excitation power. T o satisfy this requirement, green-emitting ZnS phosphors have been completely replaced by Tb'-activated phosphors (or partially by MnZt-activated phosphors). These linear phosphors, although lower in efficiency than ZnS, become brighter than ZnS:Cu, Au, Al at a current density of more than about 10 pA/cm2. The choice of green phosphor has shifted successively with time. At first, the well-known efficient X-ray phosphor Gd,0,S:Tb3' was employed with increased Tb3' concentration. Then, it was superseded by YzOzS:Tb3+because of its inferior temperature dependence. At present, the candidate host materials for Tb3' are Y3A150,,,Y3(AI, Ga)5012(Ohno and Abe, 1985); Y,Si05 and LaOCl (Tsuda et al., 1984). For projection tubes, the usefulness of Zn,SiO,: M n 2 + ,whose emission color is best fitted to the green primary, has again become of interest, though its persistence still presents a problem. As a compromise, the mixture of Y3A150,z:Tb3t(90";) and ZnzSi0,:Mn2' (10%) is used (Yamamoto e f ul., 1985). has been replaced by Yz0,:Eu3+ because The red-emitting YzOzS:Eu3+ of its inferior efficiency at high temperatures.

' By T. Kano

3 14

TAKASHI HASE et a/.

The major problem at present is the blue primary. As mentioned before, only ZnS:Ag,CI has retained its position as the blue primary for TV. For this material, although replacement of C1 by Al, with increased activator concentration, has produced a significant improvement of linearity (Hase et al., 1987), this is still not satisfactory. Since linear phosphors are now employed for green as well as red projection tubes, the saturation of the blue ZnS phosphor becomes conspicuous, as evidenced by a slight tint added to the bright white light produced by mixing the three primaries. In the case of images projected through plastic lenses, the resolution suffers from chromatic aberration if phosphors with a broad emission band are used. Thus, it is one of the most important objectives of phosphor research to obtain a narrow-band linear blue phosphor. In this respect, the single-line emission of ZnS:Tm3+ looks attractive (Shrader et al., 1971). Unfortunately, the emission from this material saturates with increased excitation level.

D. Oscilloscope Tubes' The prototype of the cathode-ray oscilloscope dates back to the invention of the CRT itself by K . F. Braun in 1897. Although built and used by many research workers in the years following, oscilloscopes were first introduced commercially only in the early 1930s by the DuMont Company in the United States. More modern oscilloscopes appeared on the market in 1947, when Tektronix, Inc. developed its first 10-MHz oscilloscopes. Continuously improved since then, oscilloscopes have remained the most popular and powerful tool for monitoring transient electrical signals. An important requirement for the phosphor screen of an oscilloscope tube is high brightness capability. For direct visual observation, green-emitting phosphors are favored because of their spectral match to the human eye. For photographic recording, blue-emitting phosphors are used because of their good spectral match to silver-halide photographic films. Another requirement for the phosphor is a persistence that is in accord with the repetition rate of the electron-beam trace. In order to observe a rapid change of phenomena repeated at a high frequency (up to 1 GHz) properly, the phosphor must respond to the changes of a rapidly moving electron beam, i.e., it must have a short decay time. By contrast, a long-persistence phosphor is useful for monitoring single-shot fast phenomena or phenomena occurring at low repetition frequency, since the trace of the electron beam can be seen for an extended time by the afterglow of such a phosphor. Oscilloscope phosphors and their properties are listed in Table 111. The

* By H. Yarnarnoto

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES

315

TABLE III PtK)SPHORS FOR OSC ILLOS(‘0PE

TUB1.S

Chemical composition

Phosphor designation

Emission color

Persistence (IO”,, peak)

Zn,SiO,:Mn Hex. ZnS: Ag, Cu, CI

PI P2

25 ms 30- I00 jis

Hex. ZnS:Ag, C1 + (Zn,,Cd,,)S:Cu, Al Cub. ZnS :Ag, C1

P7

PI I

green yellowish green blue + yellow afterglow blue

Cub. ZnS:Cu, CI

P3 1

bluish green

10’ ms

30-100 ps 40 jts

Application general use high-frequency region low-frequency region photographic measurements general use and photographic measurements

green ZnS:Cu (P31)and Zn,SiO,:Mn’+ ( P l ) are probably the most popular phosphors for displaying traces containing information in the normal frequency range of 10 Hz to 100 MHz. A recent trend in oscilloscopes is their use for observing increasingly highfrequency phenomena. However, as the writing speed of the electron beam is increased without increasing the repetition rate, the brightness of the phosphor screen is decreased. To overcome this problem, the final anode voltage is increased from the more conventional level of 3 k V up to 10-20 kV, usually by applying the high voltage only to electrodes beyond the deflection region (postaccelerating method), thus minimizing the reduction in deflection sensitivity. In such high-frequency oscilloscopes, P2 (Zn, Cd)S:Cu or P31 (ZnS:Cu) phosphors are used because of their short persistence (about 30 to 100 ps to 10% decay time). They are also superior to P1 in luminescent efficiency at high voltages. There is also a trend to provide oscilloscopes with a multifunction capability. For example, recent types of oscilloscopes can perform simultaneous recording of as many as eight pulse parameters, including, for example, pulse widths, frequencies and rise times, and also the automatic set of the best conditions for the signal display (Andrews, 1986). In association with this trend, multicolor displays are required instead of the conventional monochrome type. A color CRT with a shadow mask can be used for this purpose (McCormick, 1969). However, the frame frequency must be increased to 40 kHz from the conventional 50 to 60 Hz in order to improve the visibility of high-frequency signals. A unique display system that produces color images by means of a monochrome CRT has been developed by Vatne rt ul. (1983). This system is

316

TAKASHI HASE et al.

CIRCUITS

DRIVER

T-

R,G PHOSPHOR

C 0 LOR POLARIZER

A 1 2 LC RETARDER

POLARIZER

FIG. 19. A schematic diagram of the multicolor display system using a combination of a monochrome CRT with a liquid crystal (LC) half-wavclength retarder and polarizers. R, G, and W stand for red, green. and white light, respectively. For its function. see text. [After Vatne et d.,1983. Permission for Reprint, Courtesy Society for Information Display.]

schematically shown by Fig. 19. The CRT, specifically developed for this system, has a screen consisting of a mixture of red and green phosphors. In operation, information corresponding to the red and green components of the image is sequentially written on the screen during successive scans. By means of a set of color-selective polarizers, a large-area liquid crystal switch and a linear polarizer covering the screen, one or the other of the phosphor emission colors is transmitted in accordance with the voltage applied to the liquid crystal. (For details see Vatne et al., 1983, and Buzak, 1983.) The selection of phosphors for this system is based on several criteria as mentioned by Petersen (1983). To prevent undesired color mixing, their persistence should be short enough so that the emission decays before a color field is switched. Phosphors with a high efficiency are also necessary since the polarizers and the liquid crystal switch attenuate the emission intensity by a factor of 10. In addition, the emission spectra should match the transmission spectra of the dyes used in the color-selective polarizers, and the color difference betweeen the two phosphor components should be large. Also, it is desirable that each color be pleasing to the eye. Selected combinations of phosphors are red Y z 0 3 : E u 3 + or Y 2 0 2 S :Eu3+ used in conjunction with green Gdz0,S:Tb3+,ZnS:Cu or Y,O,S: Pr3+.

E. Tubes for Special Applications Requiring Very Short Persistence' Ultrafast-decay phosphors are used in several special tubes where it is necessary to accurately sense the beam location. Among these are beam index

' By T. Hase

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES

317

tubes, CRT computer terminals making use of light pens and flying spot CRTs.

1 . Beam-Index Tubes The beam-index tube has been of continuing interest since it enables color images to be produced by means of a single gun and without a shadow mask. The large energy losses caused by interception of electrons by the mask and the color impurity caused by thermal expansion of the mask are thus avoided. The fundamental structure of the beam-index system has been described by Morrell rt al. (1974),Matsushita (1979)and Inoue et 01. (1983) and compared with the shadow-mask system. The beam-index system can be divided into two different types. One is the ‘‘Apple” system, using periodic vertical secondary-emissive (for example MgO) index stripes, while the other uses phosphor index stripes. When struck by the scanning beam, the beam index stripes must generate a “beam-index signal” indicating the horizontal location of the electron beam on the phosphor screen. Beam-indexing systems using phosphor stripes have the advantage compared to secondary-emission systems that the index signal current (produced by the phosphor light) drops to zero when the spot leaves the index stripe. In practice the beam-indexing phosphor is deposited on the gun side of the aluminized phosphor screen, preventing its light emission from reaching the viewer. A photomultiplier mounted behind ti window in the funnel coating of the tube then generates the index signal from the light emission of the beam-index phosphor stripes (Morrell rr L J ~ . 1974). , The information on the beam location is then fed back to control the color and brightness signals, which in turn modulate the intensity of the beam. In principle, the scanning beam excites each of three primary color dots or stripes with a proper intensity in time sequence, thus reproducing color images correctly. Since the beam traverses a phosphor dot or a stripe within lo2 ns, it is necessary that the phosphor have an extremely short decay time of about several tens of nanoseconds. Frequently phosphors that emit in the ultraviolet (UV)region, typicallyY,SiO,:Ce(EL,,, -415 nm)and YAIO,:Ce(II,,, -370 nm), are used, since the UV emission can be easily separated from the visible emission. A fast-decay phosphor that emits in the infrared region would be preferred to provide a better spectral match to Si photodiode detectors. However, such a phosphor is not commercially available at present. In some cases, a green-emitting phosphor, Y,Al,O,,:Ce or Y,(AI, Ga),O,,:Ce, is mixed with the normal green phosphor, P22G, in order to improve the spectral match. Various characteristics of beam-index phosphors are shown in Appendix 1 under “Terminal Display Tubes.”

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TAKASHI HASE et al.

It should be noted, however, that the beam-index tube is, at the present stage, still inferior to the shadow-mask tube both in picture quality and cost. Additional information can be obtained by consulting reviews by Bril et al. (1971), Morrell et al. (1974), Inoue et al. (1983), Ohkoshi et al. (1981), Kaneko et al. (1978), Matsushita (1979) and Hasker and Klerk (1973). 2. Terminal Displays Using Light Pens A light pen is a tool used to identify a portion of an image on a CRT screen that may display, for example, a menu of a computer program. Instead of using a keyboard, one then selects the desired portion of a menu by placing the light pen in contact with the corresponding portion of the screen. The light pen is composed of'an optical fiber coupled to a photodetector which senses UV light locally produced by the electron. Location of the pen on the screen is indicated by determining the time elapsed from the starting point of the beam scan to the moment it is sensed. For proper functioning, the CRT screen must thus contain a phosphor with a very short decay time, for reasons similar to those for the beam-index tube. Phosphors suitable for light pens are thus essentially the same as those for beam-index tubes. See also Masuda et al. (1981) and Masuda et al. (1982). An example of such a phosphor is yellow-emitting Y,A1,OI2:Ce mixed with about 10% by weight of green-emitting Zn,SiO,: Mn, As. 3. Flying-Spot Scanner In the usual flying-spot scanner, a raster pattern of constant intensity is traced out by an electron beam on a cathode-ray tube with a flat phosphor screen. This raster pattern is then projected on to a cinefilm or slide transparency. The transmitted light, modulated in intensity by the film or slide, falls on the photocathode of a photomultiplier tube that delivers an output current proportional to the intensity of the transmitted light. This time-varying output current constitutes a video signal that corresponds to the image on the slide. In a flying-spot scanner for color television, the light transmitted by the film or slide is separated by means of dichroic mirrors (and lenses) into red, green and blue components, each of which is detected by a separate photomultiplier tube. In this case, a phosphor screen must be used whose emission spectrum covers the entire visible range. To reduce blurring of the video signal as much as possible, the decay time of the phosphor must be, at most, of the same order of magnitude as the time taken by the electron beam to scan a picture element of a diameter corresponding to the cross-section of the beam itself. It can be deduced from this that the decay time should not be much greater than about 50 ns.

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In the past, green luminescent ZnO was frequently used for monochrome images. Since the emission band of this phosphor is very broad, it can also provide light components in the red and blue. The decay time of this phosphor, however, is about 1 ps, which is too long. Although the effect of an excessively long decay time can be compensated for by means of electronic circuits, this can only be done at the expense of the signal-to-noise ratio. Recently, a mixture of Y,AI,O,,:Ce and Y,SiO,:Ce and, in some cases, a phosphor combination of Y,AI,O,,:Ce and Y,SiO,:Ce have been used. These phosphor mixtures (called P48) are white-emitting and have a decay time of about 100 ns (Bril et al., 1971).

F. Vacuum Fluorescent Displays" In vacuum fluorescent displays (VFDs), electrons emitted from local areas of an extended cathode are used to excite corresponding local areas of an adjacent phosphor screen, resulting in a relatively thin, flat display structure. An essential aspect of VFDs is the fact that the phosphor is excited by lowenergy electrons with an accelerating voltage usually below 100 volts. At such a low voltage, negative charging of the phosphor screen may become serious (see Section 111). The aluminizing technique, used in conventional CRTs, however, cannot be used here, because the low-energy electrons cannot penetrate the Al film, which must be a few hundred nanometers thick. I t is thus essential to use phosphors that have a low electrical resistivity. Also, since the penetration depth of electrons of 100 eV or lower is only about 1 nm, the emission efficiency near the surface of the phosphor particles must be high. In addition, it is important that the cathode not be damaged by interaction with the phosphor materials (Kikuta and Shimojyon, 1985). The only phosphor available for use in early VFDs satisfying these conditions was ZnO:Zn, which emits a bluish green color (Kaisel, 1954; Pfahnl, 1962; Kazan and Pennebaker, 197 1 ; Kramer, 1976). There are three methods for obtaining electrical conductivity in phosphor screens. These are summarized below. ( 1 ) Use of a conductive material as the phosphor host-for example, Z n 0 : Z n or Sn0,:Eu3+ (Matsuoka et ul., 1978, 1983). (2) Mixing of particles of conductive material such as ZnO, In,O, or SnO, with conventional insulating CRT phosphors-for example, ZnS: Ag In,O,, ZnS:Cu,AI In,O, (Hiraki et al., 1976; Narita et al., 1980) and Y,O,S:Eu + SnO,. (3) In the case of ZnS, doping of phosphors with donor ions (Al) and

+

+

lo

By T. Hase

320

TAKASHI HASE et al. TABLE IV CHARACTERISTICS OF VFD PHOSPHORS'

Composition

Color

Wavelength at peak (nm)

Color point XIY

Luminous efficiency (Im/W)

ZnO :Zn ZnS:Ag + In,O, ZnS: Cu, Al + In,O, ZnS:Au, Al + In,O, (Zn0.27Cd0.73)S: Ag In,O, SnO,: Eu

green blue yellowish green

SO5 450 $30

0.24/0.43 0.16/0.06 0.2910.59

13 0.4 3.1

yellow green reddish orange

555

0.38/0.57

3.8

665

0.6410.35

1.4

reddish orange

590

0.60/0.39

0.4

~

+

Anode voltage is about 20 V and average anode current density is about 2 mA/cm2 (Kikuta and Shimojyo, 1985)

extraction of acceptors by Zn treatment-for example, ZnS:Zn, Al (Katayama et al, 1975; Nakayama and Endo, 1976). In the case of multicolor VFDs, phosphor screens produced by method 2 are most effective and are widely used in many VFD structures. Characteristics of typical VFD phosphors are shown in Table IV. Unfortunately, compared to ZnO:Zn, all the other phosphors have much lower efficiencies. For further details of VFD graphic displays and automotive applications, see reviews by Morimoto et ul. (1986), Kishino and Kawasaki (1986), Horigome and Miyazaki (1984) and Kiyozumi and Nakamura (1983). For producing color images, aside from ZnO :Zn, however, the various characteristics of the color phosphors, including brightness, efficiency and life (as well as damage of the cathode surface by vaporized sulfur from the ZnS or (Zn, Cd)S phosphors), require further improvement (Davis et al., 1988). G . Radar Tubes"

In radar applications the information is frequently presented in the Plan Position Indication (PPI) form. For this purpose the electron beam is scanned radially from the center of the screen, while its angular position is rotated in synchronism with a rotating antenna. Since the rotation cycle must be a few seconds, it is necessary that detected radar echoes be displayed on a phosphor with a long afterglow. Otherwise, the observer would see only the bright flashes along the line being scanned. In general, it is desirable that the I'

By H. Yamamoto.

PHOSPHOR MATERIALS F O R CATHODE-RAY T U B E S

32 1

afterglow have a duration of about one rotation cycle and vanish in the next cycle. The phosphor screen most frequently used for this purpose is a double layer type, also referred to as a cascade screen (Kazan and Knoll, 1968; see also Section V1.H). The typical cascade phosphor, denoted as G M or P7, has for its top layer (electron-beam side) hexagonal ZnS: Ag, CI emitting shortpersistence purplish-blue light whose peak wavelength is at 435 nm. The cathodoluminescence of this layer excites the long-persistent photoluminescence of the underlying second layer of ZnS:Cu, CI. While the decay to & brightness of the first phosphor is only 50 p s , that of the yellowish green emission of the second phosphor, peaked at 555 nm, is more than 300 ms. The very long persistence time obtained here, although at some expense in brightness, is based on the fact that a phosphor under photoexcitation produces, in many cases, a longer persistence than can be obtained under direct electron-beam excitation. This is probably due to the larger penetration depth of photons than of electrons, resulting in a smaller volume excitation density, which, in turn, causes a larger ratio of phosphorescence to fluorescence. In addition, the parlicle size of the long-persistence layer is 10 pm or more, making use of the fact that larger crystals have a longer decay time. On the other hand, the particle size of the top layer is small (several pm) in order to reduce pinholes and intercept as many electrons as possible. Aside from their overall low efficiency, cascade phosphors are relatively expensive because of the many fabrication steps involved. Interest therefore also exists in single-layer long-persistence phosphors. Examples of such phosphors are fluorides activated with Mn2+,e.g., MgF2:MnZt (P21, P33) and their solid solutions with ZnF2:MnZt (P12) and with K F (P19,P26). These show a long orange afterglow whose decay to & brightness is as long as several seconds. However, since their efficiency falls rapidly under electron irradiation (Kotera, 1955), they are not often used for radars. In cases where brighter radar images are required and whose persistence can be controlled, tubes with conventional short-persistence phosphors may be employed with the electronically stored image refreshed at TV rates. At the same time a slowly decaying radar image can then be created by means of the solid-state scanconversion circuits.

H . Flood-Beam Storage Tubes" Direct-view storage tubes, making use of internal electronic processes, can retain a visible image on their phosphor screen for an extended time and are used for oscilloscopes, radar systems, and computer displays. Such tubes (Kazan and Knoll, 1968), in addition to a writing beam, employ a flood beam

'' By E. Nakazawa

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TAKASHI HASE et ul.

to produce a luminescent stored image. In mesh-type tubes, information is stored as a charge pattern produced by the writing beam on the insulating coating of a metal mesh positioned a short distance from the phosphor screen. The local potentials of the charge pattern on the target then control the landing of electrons from the flood gun on the phosphor screen, producing an image that corresponds to the charge pattern. The charge-storage dielectric target may consist of a nickel mesh coated with a dielectric material such as MgF,. In these storage tubes, the yellow/green-emitting (Zn, Cd)S:Ag, CI (P20) sulfide phosphor is usually used. This has a high efficiency and an emission color with a spectral peak located at 560 nm, making it suitable for visual use. Such phosphor is manufactured by heating an initial mixture of ZnS and CdS in the ratio of 6:4 at 1200°C using NaCl and BaCI, as a flux. A narrow distribution of phosphor particle sizes in the range of 6-8 pm is desired here for obtaining high-resolution images. In meshless-type storage tubes the charge pattern is created directly on the surface of the viewing phosphor. The flood beam then serves to maintain this charge pattern by secondary emission and also produces an on-off type of luminescent image. The green-emitting Zn,SiO,: Mn (PI) phosphor is usually employed here because of its good charge-storage properties as well as its desirable secondary-emission characteristics, which play an important role in the writing and storage action. This phosphor, however, bombarded by the flood-beam electrons at low voltage (<300 V) and high current density, has a rather short life because of changes in its surface state. Hurd (1974)found that low-energy electron bombardment causes a charge accumulation at the target, independent of electron energy and current density, resulting in desorption of oxygen from the surface of the phosphor. When such tubes are used in computer displays and a stored image remains unchanged for long periods, heavily excited areas may undergo noticeable deterioration in luminescent efficiency compared to other areas. Finding that the aging is a result of “electron enhanced phase transformations”, Woody (1978) subsequently showed that the incorporation of MgO substitutionally into the Zn,Si04 lattice stabilized the lattice and minimized the damaged by electron bombardment. I . Special Applications Requiring High-Resolution Screensi3

In applications of phosphor screens such as in image intensifiers, electron microscopes and photographic recording, it is essential that the phosphor particles be small in order to reproduce images with high resolution. However, l3

By T. Kano and E. Nakazawa

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323

since the luminescent efficiencygenerally decreases as the size of the phosphor particles is reduced (see Section 1I.B. I), the minimum size is practically restricted to about 2 pm. 1. Image Intensijiers In image intensifiers, X-ray images or weak optical (visible or infrared) images are converted to a pattern of photoelectrons at a photocathode, usually a multialkali metal film. These emitted electrons are then accelerated and imaged onto the phosphor screen by the electric fields of the electron lens system. Applied voltages of about 30 k V are used for X-ray image intensifiers and 9-12 kV for other intensifiers. The green-emitting ZnS:Cu, Al phosphor with a particle size of 2-3 pm is used for X-ray image intensifiers because of its color match to photographic films, while the blue-emitting ZnS:Ag ( P l l ) is used for optical-input image-intensifiers. To obtain dense phosphor screens, an electrophoretic deposition method is often employed (see Section V1.D). 2. Electron Microscope In the transmission electron microscope, electrons emitted from a point cathode are accelerated and allowed to flood a thin sample. The pattern of transmitted electrons is then focused on a phosphor screen viewed from the gun side, producing a luminescent image of the sample. The accelerating voltage in these systems is in the range of 100-3000 kV (the upper value being used for special applications). Green-emitting (Zn,Cd)S:Cu, A1 with small particle size of 2-3 pm is used for this purpose because of its color matching to photographic films. Because sulfide phosphors with such particle sizes are only half as efficient as those with 6- 10 pm particles, it may be possible that nonsulfide phosphors with small particle size will replace sulfide phosphors, since their efficiency is less dependent on particle size than in the case of the sulfides. 3. Photographic Recording In CRTs used for printing, an electron beam modulated by electrical signals scans a single line on the phosphor screen. An image is then reproduced on a sheet of photosensitive materials, such as photographic paper or a photoconductor, by mechanically moving it in a direction perpendicular to this line. Blue-emitting ZnS: Ag (PI 1)phosphor peaked at 450 nm with a decay time of 30-100 p s is generally used for this purpose, since its emission color is suitable for photographic paper as well as the photoconductive layers of ZnO and Se used in electrophotography. Using an electrophoretic deposition

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method for the phosphor (see Section V.D) and a fiber-optic face-plate for the CRT (avoiding a projection lens), images with a resolution as high as 20 lines/mm have been obtained. For reproducing a color TV picture (video hard-copy) on photographic film (Okuda and Ohno, 1985),a special CRT has been devised whose screen is composed of only three stripes: a red-emitting stripe of Y,O,S:Eu (P22-RE3) phosphor, a green stripe composed of the white-emitting P4 phosphor and a green filter, and a blue stripe composed of the P4 phosphor and a blue filter. J. Small Monochrome Tubes14

Small flat tubes with 4- to 6-inch screen size and 30- to 42-mm thickness have been developed in response to the demands of new applications such as TV telephone, door phone, and kitchen TV (Sato et al., 1983; Kanatani, 1985; Yoneda and Utsumi, 1987). In these tubes the screen is inclined nearly parallel to the electron beam, and the image is observed from the electron-bombarded side of the screen (rear-view type). Although rear viewing gives a 30% higher brightness than conventional viewing through the opposite side of the phosphor screen, a high degree of smoothness is required for the phosphor surface. A white-emitting Y,0,S:Tb3+ (P45) phosphor is used instead of the white-emitting sulfide phosphor (Zn,Cd)S: Ag (P4) phosphor because of concern with Cd-pollution. While the P45 phosphor has a somewhat lower brightness compared with the latter, it has several advantages over the sulfide phosphor. It can withstand the ion bombardment that tends to occur in such small tubes, and it has a shorter decay time, making it free from undesired afterglow. In practice the phosphor screen is fabricated on a conducting graphite underlayer using the rotating- or flow-coating method instead of the settling method usually employed for monochrome screens, since it provides a smoother surface for the phosphor screen. Such 4- and 6-inch flat monochrome CRTs, whose picture quality may be equal to or better than that of conventional CRTs, may have a resolution of 1000 x 500 TV lines (Yoneda and Utsumi, 1987). Much smaller, more conventional miniaturized CRTs with 0.7-inch screen size have also been manufactured for use as the viewfinder in home video cameras (Taniguchi et al., 1987). In these a fine screen is produced by employing the centrifugal-settling method and using fine-particle (3-micron) phosphor (P45). However, the phosphor is not aluminized, since this often causes wrinkling of the surface. l4

By E. Nakazawa

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES

v.

METHODSUSED

325

FOR SYNTHESIS OF PHOSPHOR POWDERS'5

In this section, some typical methods of phosphor preparation are described. It should be recognized, however, that for any particular type of phosphor, various methods of preparation are known. In addition it is assumed that individual manufacturers have their own proprietary methods of preparation. In part A general discussions of phosphor preparation processes are provided, while in Part B the synthesis of some specific CRT phosphors is discussed. A . General Procedures

The general processes of phosphor powder preparation can be divided into three parts. The first involves purification of the raw materials and synthesis (in a narrow sense) of the constituent phosphor compound (chemical reactions). The second involves the growth of phosphor particles by firing (crystal growth), and the third involves the treatment of the fired phosphor powder to make it suitably luminescent for CRT use.

I. Chemical Reactions before Firing An example of the first process involves precipitation of ZnS from a solution. For this purpose ZnO powder is put into about 0.1 N sulfuric acid, producing an aqueous solution of ZnSO,. Then, in order to eliminate impurities, such as Fe, Co, Ni, etc., which reduce the luminescence efficiency, H,O, and diluted NH,OH are added to purify the ZnSO,. For example, Fe is removed in the form of insoluble hydroxides such as Fe(OH),, with the most suitable pH value being about 5-6 (Leverenz, 1950).Next, H,S gas is bubbled into the aqueous ZnSO, to convert it to insoluble ZnS. These reactions are expressed as ZnO

+ H,SO,

ZnSO,(aq. sol.)

=

ZnSO,(aq. sol.)

+ H,S

=

ZnSJ

+ H,O

+ H,SO,

Fe2+ + Fe3+ + Fe(OH),J

cu2+-+ CUSJ. Pure zinc sulfide is obtained after washing with deionized water to remove excess H,SO,.

Is

By T.Hase

326

TAKASHI HASE et al.

FIG.20. Scanning electron microscope photographs of particles of ZnS raw material. Each particle, about 3 pm in size, consists of many crystallites.

The shape, size and crystal quality of the precipitate particles strongly depend on the reaction conditions, such as pH, temperature, concentration and agitation processes of the ZnSO, solution and coexisting ions. (More details are given by Abrahams and Buiocchi, 1988.) Figure 20 shows a scanning electron-microscope photograph of the particles of ZnS raw material. In the case of Y 2 0 3: Eu phosphor, precursors are formed by precipitation reactions as follows: 4( 1 - x)Y(NO,),(aq. sol.) + 4xEu(N03),(aq. sol.) = 2(Y,, - x ) ,

+ 3(COOH),(aq. sol.)

+

EuX)2(C00),1 12HN03.

The reaction conditions affect the shape, size and crystal quality of the precipitate particles similarly to the ZnS formation. Heating of the suspension promotes crystallization of the resulting precipitate. The oxalate precipitate is then fired in air to produce the corresponding oxide. In this way, rare-earth activators (for example, Eu or Tb) can be homogeneously mixed in yttrium oxide. For oxide-based phosphors, a higher concentration of impurities can be tolerated; about 10 pg/g is often acceptable (Hill, 1984). The optimum activator content usually ranges from 0.0001 mole (for example, Ag, Cu, Au in ZnS) to 0.01 mole (for example, Mn, Eu, Tb, Ce) per mole of host crystal.

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2. Synthesis of' Host Materials Further growth of the microcrystals is achieved by high-temperature firing of the precipitate. Diffusion of the component ions in solids is, as a first approximation, believed to reach a significant level at a temperature about f of the melting point (in "K), of the compound. In the case of crystals having a melting point of 2000°C (2273°K). for example, growth occurs above 1240°C ( - 2273 x f 273). However, such high-temperature firing often results in sintering of the fired products and requires ball-milling to produce a well-dispersed powder. One of the best methods to produce a well-crystallized and well-dispersed powder is to add a flux (mineralizers or sintering aids) during the firing processes. Since the flux has a relatively low melting temperature, it contributes to the crystal growth by dissolving a part of the raw materials or products into their melts, thus accelerating the diffusion of constituent ions at a reduced temperature. As well as additive ions, the component raw materials themselves act as fluxes. In other cases, the fluxes are produced during the firing process. A well-dispersed powder is then obtained from the cooled product by dissolving away the flux with an appropriate solution (usually an aqueous acid or alkaline solution). The most popular fluxes are water-soluble, low-melting-point alkali or alkaline-earth halides, borates and sulfates, which are usually added in amounts on the order of 1 wt of the host crystal (Leverenz, 1950). Typical examples of the flux processes are as follows:

'x

+

(1 - x)Y203 xEu203 =

2(Y,

+ (1 + y)V,O,

Eu,)VO,(phosphor powder)

+ yV,O,(flux)

+ 6NaOH(aq. sol.) = 2Na3V0,(aq. sol.) (1 - x)Y203+ x E u 2 0 3 + (1 + y ) S + zNa,C03 -,(Y1 -,, Eu,),O,S(phosphor powder) + Na,,S(flux) Na,,S(solid) + H,O -,Na,,S(aq. sol.) V,O,(solid)

The materials to be fired in air are packed into a container made of quartz, alumina or silicon carbide, usually provided with a tight cover. The cover prevents vaporization of the fluxes as well as contamination with dust from the furnace. The temperature of the furnace should be as uniform as possible and should be controllable within at least & 10°C,since many phosphors are very sensitive to a small change in temperature during reaction and crystallization.

328

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A suitable firing time is about 0.5-6 hours, depending on the volume of the furnace, size of the container and quantity of the phosphor powder charge. The firing atmosphere, which may consist of neutral gas (for example, N,, Ar), reducing gas (for example, C , N,-max. 10% H,) or oxidizing gas (for example, O,), can change the emission color by its effect on the valency of activators such as Eu, Tb, Ce, or Mn. It can also affect the efficiency by controlling defects occuring in the host crystal. The heating and cooling processes also influence the diffusion of the activator. Of course, the firing processes involved should be appropriate for mass production of over 10 tons of phosphor per month. For mass production, the raw material containers are preferably charged on belt conveyors moving through tunnel furnaces. This system, however, places a limit on the heating and cooling rates of phosphors.

3. Treutments ajier Firing After firing, several further operations may be required. The removal of fluxes has been described in Section 2 above. In most cases, it is necessary to break up coagulated phosphor grains of a fired product by milling. In general the milling is done, for example, by ballmilling, using an alumina or a china-ball milling pot with balls of different sizes (about 1-10 mm in diameter). In an ideal case, the phosphor slurry mixed with balls occupies more than half the volume of the ball-milling pot used to disperse the grains. A common way to prepare a slurry is to provide the phosphor and balls in the same quantitative ratio, then convert the mixture to liquid slurry by the addition of water. The rolling rate ranges from several revolutions per minute (in the case of ZnS) to several tens of revolutions per minute, depending on the phosphor characteristics (for example, the degree of particle coagulation and particle size). It should be emphasized, however, that ball milling should be avoided if possible (especially in the case of sulfide phosphors), since the phosphor particles are damaged by the mechanical action of the grinding process (Tajima and Takagi, 1974; and Sekine, 1974).This causes, to some degree, the destruction of crystals, leading to a decrease in the luminescence efficiency. Since phosphor particles about 6-10 pm in size are required for general purposes, and about 2 - 5 pm in size for high-resolution screens, suitable processes are then used to select a restricted ranges of particle size. For mass production, this may be achieved by using the variation in sedimentation rate expressed by Stokes’ equation. Finally, various kinds of treatments may be applied to improve the

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deposition of the phosphor powder as a uniform screen. These may involve coating the surface of the fired phosphors with inorganic materials such as S O , , ZnO, Zn(OH), and Al,O,. Essential properties of phosphors required for screening processes are a dispersion sufficient for homogeneous screening and an adhesion sufficient for making patterned screens by photodeposition techniques. These two requirements are in trade-off relationship with respect to each other, with compromises made by adjusting various parameters such as coating of the phosphor surfaces and addition of surface active agents in slurries, as well as ball-milling. In general, large particles are more dispersive and less adhesive than smaller particles. These parameters depend on the manufacturer, with the phosphors being tailored for a specific user. In particular, fine patterns are required for high-definition color CRT displays. As a consequence, the development of techniques to disperse small particles without damaging them is an important aim. B. Preparation of Some Widely Used Phosphors

Examples of the general processes used for preparing important phosphor powder preparations-namely sulfide, oxysulfide and oxide phosphors-are described in greater detail below. 1. Blue-Emitting Z n S : A g and Green-Emitting Z n S : Cu.Al Phosphors

First, a high-concentration solution of silver nitrate is added to zinc sulfide at a ratio of about 1000 p g / g of ZnS. The mixture is then dehydrated and further dried. Following this, pure ZnS and ZnS mixed with a high concentration of Ag are mixed by ball milling with some fluxes-for example, about 0.1 wt of NaCl, MgCI,, etc. The materials are then fired at a temperature in the range of 800 to 1000°C in a sulfurizing atmosphere, produced by S, H2S or CS,. The resultant fired cake is sieved through a nylon screen in water. The sieved blue phosphor ZnS:Ag is mixed with a solution of surfaceabout treatment agents-for example, SiO,, Zn(OH), , ZnO or Al,O,-at several hundred p g / g of ZnS. After water-soluble impurities are removed by washing, the phosphor is dried and passed through a sifter. Green phosphor is obtained by a process almost similar to that for the blue phosphor, except that in place of silver nitrate, copper sulfate is used (Rothschild, 1963; Miyagawa et a/., 1970; Matsuura et al., 1977). Figures 2 1 and 22 show typical scanning electron-microscope photographs of the particles of blue- and green-emitting CRT phosphors, respectively. (For a discussion of pigmented phosphor such as that shown in Fig. 21b, see Section 1X.C below.)

330

TAKASHI HASE et al.

(a)

(b)

FIG.21. Scanning electron microscope photographs of particles of ZnS: Ag phosphor (a) without pigmentation; (b) pigmented particles (see Section IX. C).

(a)

(b)

FIG.22. Scanning electron microscope photograph of particles of ZnS:Cu, AI phosphor (a) without coating; (b) Si0,-coated particles.

P H O S P H O R MATERIALS F O R CATHODE-RAY T U B E S

33 1

FIG.23. Scanning electron microscope photograph of particles of Y 2 0 2 S :E u phosphor; (a) without pigmentation, (b) pigmented particles (see Section IX-C).

2. Red-Emitting Y,O,S;Eu Phosphors Yttrium oxide, europium oxide and sulfur (about 50% oxide) are mixed with 40-507; by weight of fluxes, usually sodium carbonate and alkaline phosphate. The mixture is then fired in a covered alumina crucible at a temperature of about 1250°C.The fired product is a yellow solid retaining the shape of the vessel. The product is next settled in water for about eight hours and then sieved, if possible, and washed with diluted HCI (about 1 N) to remove the Na,S (Royce, 1968; Yocom, 1968; Royce rt al., 1970; Kano et ul., 1972; Koskenlinna et al., 1976; Ozawa, 1977; Kanehisa, et al., 1985). Figure 23 shows a typical scanning electron-microscope photograph of the particles of red-emitting CRT phosphor. (For a discussion of pigmented phosphor such as that shown in Fig. 23b, see Section 1X.C below.) 3. Green-Emitting Zn,SiO,: M n and Zn,SiO,: Mn,As Phosphors Commercial Zn,SiO,:Mn phosphors are known as P1 (without As doping) and P39 (with As doping). These phosphors are synthesized by a solid reaction of ZnO, a slight excess of SO, and/or 0.01 mol % of As,O, at a firing temperature between 1200°C and 1300°C for two hours in air. After firing, the product is pulverized, and about 0.8 mol % of MnCO, is added to it. The mixture is again fired at 1200 to 1300°Cfor two hours in air. The fired products are again pulverized and washed to obtain a phosphor represented by the formula Zn,SiO,: Mno,oo8(Aso,oo2) (Yaguchi et al., 1985).

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VI. SCREENFABRICATION TECHNIQUES'~ Screens for CRTs are generally composed of phosphor particles, 3-12 pm in diameter. For conventional applications the screen thickness is frequently 15-30 pm, about 2-4 particles deep, with a resulting weight of 3-7 mg/cm.2 The screen weight is a key parameter in the screen fabrication process. As it is increased from zero, the light emission from the gun side shows a linear increase with increasing screen thickness, and then saturates at the screen weight where penetration of the electron beam through the screen becomes negligible. The light emission through the glass faceplate, on the other hand, shows a maximum at a somewhat decreased screen weight, since the optical transmittance of the screen decreases with screen weight (Fig. 24).

TOTAL

/GUN-SIDE

G L A S S - ~DE ~

1

2

I

I

4

SCREEN

I

I

6 WEIGHT

8 ( rng/crnZ

10

1

FIG.24. Dependence of emission intensity on screen weight. The screens were made of a red-emitting phosphor Y,O,S:Eu with an average particle size of 6.5 pm. Excitation was by an 18 kV electron beaiil. [After Kano and Uchida, 1983.1

l6

By T. Kano

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In most tubes the gun side of the phosphor layer is coated with a thin metal backing (evaporated Al, 150-300 nm in thickness). This reflects light emission from the gun side of the layer to the glass side and also prevents the screen from charging during cathode-ray excitation. The optimum screen weight is thus dependent on maximizing the sum of the glass-side and gun-side emissions. In fabricating CRT phosphor screens, some screening processes pose a problem for obtaining the screens with maximum emission. In shadow mask CRTs, the phosphor screen, initially deposited as a continuous layer, is exposed to UV radiation from a point source through the apertures of a shadow mask, causing locally exposed areas to become insoluble in rinse water (see Section VI.B, Slurry Method). Because of light scattering of the exposing UV light in the phosphor screen, its intensity is decreased at the intersurface of the phosphor screen and the glass substrate. Thus, a limited number ( 2 - 3 ) of particle layers is preferred to minimize scattering, independent of particle size, to assure enough adhesive power of the screen to the substrate. As a result, phosphors with smaller particle size are screened at a lower-than-optimum screen weight in the actual manufacturing process. As an example, for screens of high-definition terminal displays, which require small picture elements of the order of 100 pm, a smaller particle size is preferred, although at some sacrifice in brightness. With present fabricating techniques, screens with larger particle size and greater screen weight tend to be brighter. The limiting factor is their lower adhesive power to the substrate panel and low yield rate. Another important point is that the phosphors should not be allowed to deteriorate during the baking process (38O-45OnC, in air and in vacuum). The purpose of this process is to eliminate by oxidation organic binders that may cause charging of screens or deterioration of the vacuum level by slow evaporation. This oxidation process sometimes results in oxidation of the phosphor materials themselves or decrease in light emission due to residual inorganic binding materials (chromium compounds).

A . Settling Method

The settling method for phosphor deposition or screening has been used since the beginning of CRT manufacturing and, surprisingly, it is still the predominant process for depositing phosphor screens in monochrome CRTs. The manufacturing process is simple, and the fabricated screen adheres well to the face plate so that it is commonly used for the relatively thick (about 6 mg/cm2) screens of projection tubes where pinholes cannot be tolerated. A typical settling procedure involves the following steps: First a “cushion” solution A is poured into the glass bulb of the CRT and

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maintained in a quiescent state. Then a phosphor suspension B from a nozzle held above the surface is allowed to flow into A, the solution A acting as a gelling agent to phosphor suspension B. A typical example of A is an aqueous The phosphor solution of barium acetate or nitrate (about 0.05 wt suspension B, for example, is prepared by suspending a phosphor in an aqueous solution of potassium silicate (about 0.5 wt % as silica). During the mixing process of A and B, hydrated silica with attached silicate ions is flocculated on the surface of the phosphor particles by the action of cations (Lines, 1964).A precipitate formation of silica outside the phosphor particle, however, should be avoided by adjusting the concentration of A and B (de Boer and Emmens, 1955). After several minutes’ settling, the phosphor particles are deposited, forming a uniform screen on the faceplate of the glass bulb. After sedimentation of the phosphor, the solution is slowly removed from the bulb by decantation, and the screen is then dried. Screens fabricated by this method have relatively rough surfaces, since the phosphor particles are not closely packed as a result of the coagulation process involved. Such loosely packed phosphor screens have been shown to have a somewhat higher cathodoluminescent efficiency, by several percent, than do closely packed screens formed from well-dispersed phosphor particles. This is explained by the more efficient capture of back-scattered electrons at a rough screen surface compared with a screen of well-dispersed particles, whose surface is relatively smooth (Kano and Uchida, 1983). Following the settling process, a thin film of aluminum is evaporated onto the phosphor surface. T o make this film smooth and reflective, the screen is first coated with a film of acryl emulsion or organic lacquer. After evaporation of the aluminum, this coating material is removed by baking. Throughout these processes, the phosphor screen must adhere well to the glass panel. Initial difficulties may arise during decantation of the solutions, since the phosphor screen when wet might not be resistant to any agitation involved in this process. Further difficulty may arise when the dry phosphor screen is wetted with a lacquer before the evaporation of the aluminum film.

x).

B. Slurry Method

In the case of shadow-mask color CRTs where the screen consists of an array of multicolored dots or stripes, the slurry method has been employed predominantly. A typical slurry method is as follows: A phosphor slurry is first prepared by mixing a phosphor powder, an aqueous polyvinyl alcohol solution and an aqueous ammonium dichromate solution. Use of some additives is recommended to eliminate bubble

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formation, to disperse the powder particles well, or to adjust the pH of the slurry. The slurry thus prepared is dispensed onto a slowly rotating horizontal glass panel, causing it to be spread homogeneously over the panel by rotation. To spin off the excess amount of the slurry, the panel position is changed from horizontal to vertical while the rotation speed is increased. The phosphor screen thus formed homogeneously over the panel is then exposed to UV radiation from a point source through the apertures of a shadow mask, causing locally exposed areas to become insoluble in rinse water. This insolubility is caused by bridging of polyvinyl alcohol chains due to an action of the photo reduced chromium ions. By rinsing away the water-soluble unirradiated parts of the screen, a pattern of phosphor dots (or stripes) is left corresponding to the shadow-mask aperture pattern. The above process is then repeated two more times, using phosphors of different colors and with the position of the light source shifted each time, to produce suitably located green, blue and red phosphor patterns, thus forming a complete multicolored phosphor screen. To avoid difficulties such as inhomogeneous screening, pinhole formation as a result of rinsing, contamination of a phosphor pattern by phosphor powders of other colors, etc., the following parameters must be adjusted: (1) Particle size distribution of the phosphors: Particles smaller than 3 pm in diameter are preferably removed by decantation before the slurry process is carried out, since they cause increased scattering of the irradiating light during the UV exposure process. Since such particles, when coated on phosphor dots of other colors, are difficult to remove during the rinsing process after irradiation, they interfere with the color purity of the resultant screen. (2) Dispersion of the phosphor particles: Coagulated particles interfere greatly with uniform coating of the slurry during rotation of the horizontal glass panel. In former times, ball-milling of slurries was employed for dispersion of the phosphor particles, resulting in a decrease in luminescent efficiency. Recently, the process has been replaced by soft ball-milling or sieving after firing of the phosphor. Supporting this advance has been the development of phosphor firing technologies that enable dispersion of fired phosphor cakes by these soft processes. This eliminates the loss of luminescent efficiency otherwise resulting from damage to the phosphor particles after firing. Phosphors that do not require slurry ball-milling are called “non-mill phosphors”. (3) Coating agents: Various water-insoluble compounds, such as silicates, phosphates, aluminates, oxides and their combinations, are frequently coated on the phosphor particles. The coating technologies used differ in

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accordance with the individual phosphor manufacturer and still remain in the realm of the private “know-how” of the company. (4) Composition of the slurries: One of the important parameters is the viscosity of the slurry, which depends strongly on the concentration of polyvinyl alcohol. Some organic additives are also used for removing bubbles and for dispersing phosphor particles. (5) Schedule for phosphor dispensing and rotation of the glass panel. (6) UV exposure conditions. (7) Rinsing conditions: In general there is a trade-off between pinhole formation and contamination by other color phosphors. The former is increased by stronger rinsing, while the latter is increased by weaker rinsing. In practice a soft shower of small water droplets is used for rinsing. C . Dusting Method

A convenient method to prepare phosphor screens is by dusting a dry phosphor powder onto a tacky surface. One of the dusting methods that has been applied to the manufacturing of multicolored CRTs of shadow-mask type is as follows: A photo-sensitive slurry composed of an aqueous solution of polyvinyl alcohol and ammonium dichromate is first coated onto a glass panel. Then a dry phosphor is dusted onto the wet panel, sticking to the surface and forming a uniform layer. Exposure of the screen by UV light through the shadow-mask apertures makes the irradiated areas of the polyvinyl alcohol insoluble, thus retaining the particles at these areas. The subsequent processes are similar to those of the slurry method. A new dry process utilizing phototackifiable diazonium salt has been recently developed (Nonogaki et al., 1986). This process is unique in that the photosensitive layer is exposed directly to UV before the phosphor is deposited. Thus it is capable of producing high-resolution phosphor patterns, since less scattering of the exposing light occurs in the absence of the phosphor. A typical process is as follows; An aqueous solution of p-diazo-N,N-dimethylaniline chloride-zinc chloride (DDMA) containing a small amount of water-soluble polymer is spread onto a glass panel and dried to form a crystalline film. The film is then exposed to light through a shadow-mask aperture. The exposed part of the film is photo decomposed, producing free zinc chloride, which absorbs water vapor from the air and becomes sticky. The phosphor dot (or stripe) screens are then formed selectively on the sticky patterns by dusting phosphor powders onto the surface followed by air blowing. Multicolor phosphor screen patterns are formed by repetition of the above processes.

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D. Electrophoretic Method In the case where especially dense monochromatic phosphor screens with small particles are required for high-resolution applications, an electrophoretic deposition method such as the following is used (McGee et al., 1966): Phosphor powders are suspended in a polar organic solution, and some cationic additives are adsorbed on them. A negative potential is applied to a conductive substrate immersed in the solution with respect to a positive electrode held parallel to the substrate. The resulting applied electric field then causes the positively charged phosphor particles to migrate to the substrate, coating its surface. A very desirable feature of this method results from the fact that, if pinholes occur, the applied electric field is stronger in these areas than in the phosphor-coated areas, causing additional phosphor particles to migrate preferentially to the pinholes. This results in uniform screens whose surface is very smooth. Well-dispersed fine powders are best suited for use in this method, since their migration is affected more by the applied electric field than by settling due to gravity. One application of the electrophoretic deposition method is for producing the high-resolution output screens required in X-ray image intensifiers or flying-spot scanners. Another application is for coating the selected electrode areas of vacuum fluorescent tubes or other flat CRTs.

VII. SPECIAL. PHOSPHORSCREENS A . Voltage- or Current-Density-Controlled Multicolor Screens”

This section describes special types of phosphors, which allow highresolution, multi-color pictures to be obtained when used in a simple CRT structure similar to that of a monochrome tube: i.e., one with a single gun and no shadow mask. There are two types of such phosphor screens. In one type the emission color is varied by a change in the accelerating voltage, and in the other it is varied in accordance with the current density. In either case the action is based on a combination of a superlinear and a sublinear (or linear) dependence of the light output upon the voltage or current density. Although the voltage-controlled type can attain a wider range of color change as compared with the current-sensitive type, the high-voltage switching circuits required are very complicated.

’’ By T. Hase

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Examples of these two types of phosphor screens are given below. 1. Voltage-Controlled Multicolor Phosphors

The variation of color is produced here by a change in the penetration depth of a suitably designed screen with accelerating voltage. The screens can be classified into three main groups as discussed below:

a. Superposed-Layered Screens This screen arrangement makes use of two luminescent layers that emit different colors. The first layer may consist of a conventional phosphor deposited on the glass substrate. A transparent, nonluminescent layer is then formed on the first layer, and above this a second luminescent layer, both made of very fine particles, is deposited. At low accelerating voltages only the second (uppermost) layer is excited. At high accelerating voltages the electron beam penetrates to the first layer, causing luminescence from this layer as well. Additional information on this subject can be obtained in Morrell et al. (1974). In practice, however, it is difficult to accurately control the thickness of the layers to realize the desired color change. Improvements in this respect can be obtained by using, instead of phosphor powder layers, luminescent thin films prepared by evaporation or surface reaction. These also permit obtaining high contrast (see also Section VII,B,2). b. Mixed-Phosphor Screens Such screens are made of a uniform mixture of a phosphor powder of one color with a phosphor of another color whose particles are coated with an inefficient surface layer (a dead layer) formed either by deposition of a nonluminescent material or by diffusion of killer impurities such as Co, Ni or Fe into the phosphor. This surface layer increases the threshold voltage of luminescence of these particles. Since there is a large difference in the threshold voltage between the two phosphors in the mixture, it is possible to vary the emission color of the screen. An example of a screen mixture is green-emitting (Zn,Cd)S:Ag,Co, which has a high threshold voltage or superlinear characteristic because of the addition of Co, mixed with small particles of red-emitting YV0,:Eu (less than about 3pm in diameter). The green phosphor is prepared starting with (Zno,,Cdo.3)S:Ag (100 pg/g). This is agitated in an acetone suspension containing cobalt chloride (CoC1, 6H,O). The phosphor suspension is then dried slowly with occasional stirring and sieved. A batch of the phosphor, packed into a small quartz tube, is fired rapidly at a temperature of about 800°C for 15 minutes in air. After firing, the sample is examined by ultraviolet (UV) excitation, and any material that does not luminescence is removed. The phosphor is then washed with deionized water,

-

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resulting in a material of composition (Zn,,,Cd,,,)S: Ag (100 p g l g ) , Co (500 pglg). The green-emitting phosphor and red-emitting phosphor YVO,: Eu are then mixed in a 1 O : l ratio by weight. Under electron bombardment the emitted light is red at 5 kV, reddish-orange at 8 kV, orange at 10 kV, yellow at 13 kV, and yellowish-green at 18 kV. c. Screens of Onionskin Phosphor Particles In this arrangement each phosphor grain consists of a core particle surrounded by a barrier layer that is then coated with a number of small particles of a second phosphor layer. Examples of this are green-emitting (Zn,Cd)S:Ag,Co or Zn,SiO,: Mn,Co core materials (with a superlinear characteristic) coated with small particles of redemitting YV0,:Eu about I pm in size (about 1 O : l by weight) using acrylic binder. Using (Zn,Cd)S:Ag, Co, for the green phosphor, the following brightness and color were obtained using a 12-inch CRT: 0.4 ft-L of reddish orange (x = 0.613, y = 0.345) at 10 kV, 1.0 ft-L of orange (x = 0.508, y = 0.425) at 13 kV, 1.7 ft-L of yellow (x = 0.438, y = 0.476) at 15 k V and 3.5 ft-L of yellowish-green (x = 0.380, y = 0.524) at 18 kV. (Emission spectra and x and y coordinates of such phosphor powders are shown in Figs. 25 and 26.) Figures 27a, 27b and 27c illustrate the three types of phosphor structures. For reviews on this subject, see Messineo and Thomsen (1966), Prener and Kingsley (1972), Calves (1 979), Martin (1973), Ueba et al. (1974) and Shiraishi et al. (1980).

--

1.0

+ C

f

e

0

v

a +

E 05

2 C

U

C

P u) B

E

w

00

400

500

600

700

8 0

Wavelength (nm 1 FIG.25. Cathodoluminescence emission spectra of green-emitting (Zn, Cd)S:Ag, Co phosphor particles coated with red-emitting YVO,: Eu particles. For an operating voltage of 10 kV, color coordinates were x = 0.613, y = 0.345; for 13 kV, x = 0.508, y = 0.425; for 15 kV, x = 0.438. y = 0.476;for 18 kV, x = 0.380, y = 0.524.

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400

500

700

600

0

Wavelength (nm) FIG. 26. Cathodoluminescence emission spectra of green-emitting Zn,SiO,: Mn, Co phosphor particles coated with red-emitting YV0,:Eu particles. For excitation with an operating voltage of 8 kV, color coordinates were x = 0.584, y = 0.349; for 10 kV, x = 0.545, y = 0.397; for 13 kV, x = 0.467, y = 0.470; for 15 kV, x = 0.407, y = 0.527; for 18 kV, x = 0.353, y = 0.575.

Red phosphor

Green phosphor

Barrier layer (a)

(b)

Glass substrate

Glass substrate Green phosphor /

Red phosphor

Glass substrate (C)

FIG.27. Schematic examples of some idealized penetration screens: (a) superimposed-layer screen; (b) mixed-phosphor screen; (c) onionskin phosphor screen.

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES

34 1

2. Current-Sensititw Multicolor Phosphors Screens of this type make use of a mixture of a phosphor powder whose luminescence, for example, is superlinear with respect to current density, and a phosphor powder that is sublinear or linear. Depending on the current density of the electron beam, the color of one or the other phosphor can be made to predominate. A combination of Zn2Si0,: Mn as a green-emitting, sublinear phosphor and (Zn, Cd)S:Ag, Ni as a red, superlinear phosphor was studied, for example, by Avella (1970b). Although some CRT’s using such phosphors were developed between 1968 and 1972, they were not put to practical use because of their limited brightness and color gamut. The effort of these years has been reviewed by Sisneros (1970), Sisneros et al. (1970), Avella (1970a), Tecotzky (1971) and Hirota et al. (1972). Recently, Ohkoshi et al. (1982) investigated a new CRT of this type that provides a wider color range of red and green by using Y,O,S:Eu, Ce and ZnS:Cu, Al, Co, respectively. The sublinear red-emitting Y,O,S: Eu, Ce (Ce 8 pg/g) phosphor and the superlinear green-emitting ZnS:Cu, Al, Co (Co 6 pg/g) phosphor were mixed in a weight ratio of about 15:85. The brightness of a 9-inch CRT with such a screen was about 140 nit at 18 kV and 1 pA/cm2 time-average beam current. The color varies from red at 0.4 pA/cm2 to amber-green at 4 pA/cm2. Tubes with such screens are expected to be useful for computer output terminals.

--

B. Thin-Film Screens 1. Potential Advantages of Luminescent Thin Films

The advantages of cathodoluminescent thin films were elucidated as early as 1947 by Williams. In the 1950s and 1960s, the expectation that new CRTs would emerge with transparent and high-contrast screens encouraged many investigations on the preparation of phosphor films using materials such as ZnS, CaF,, Zn,(PO,),, Zn,SiO, and MgSiO,, all doped with Mn2+,as well as undoped CaWO, (Feldman and O’Hara, 1957; Feldman, 1958) and ZnO (Pashley, 1956). Neglecting the problem of light trapping (see below), the intrinsic efficiencies of these films were found to be nearly one order of magnitude less than those of powders with the same chemical compositions (Goldberg, 1966) except for ZnS:Mn films, which can be about 85 to 90% as efficient as a thick powder layer (Feldman and O’Hara, 1957). Because of such low efficiencies, the practical application of such thin films was limited. By H. Yamamoto

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However, great progress has been made in thin-film preparation and analysis techniques during the last decade for other applications. For example, the main techniques of film preparation in the 1960s involved the evaporation of a material in vacuum by filament heating or chemical vapor deposition in the case of ZnS and CdS (Studer and Cusano, 1955). Now evaporation by electron-beam heating and sputtering in a gas plasma are the most popular techniques. We can also point to the progress made in other technologies relating to thin film preparation. First, the capability to control the gas flow rate precisely has been increased, making it possible to regulate the flow rate with electronic instruments to values as small as 1 ml/min within an error of a few percent. Second, the purity of the starting materials has been improved. Third, progress in vacuum pumps has made it possible to produce an oil-free atmosphere as low as lo-" torr relatively easily, compared to the earlier level of 1 0 - 6 torr associated with conventional oil-diffusion pumps. With the aid of these new techniques, which are still improving, we can thus control the atmosphere of the film preparation chamber more precisely than before. With an ultrahigh vacuum (slO-'o torr) we can also use a molecular beam in evaporation system. Such progress in these areas has supported investigations to improve luminescence efficiency or to provide new display functions of thin-film screens. Compared with powder screens, luminescent thin films have the following two fundamental advantages: (1) The film can be transparent or translucent with low diffuse reflectance. Because of their small light scattering, such films enable high image resolution to be obtained, limited only by the spot size of the electron beam. (2) The dissipation of heat generated in the phosphor by electron-beam bombardment is much improved because of the good thermal conductivity of the thin-film screen medium itself, as well as the good thermal contact between the screen and the substrate (faceplate). However, thin-film phosphors, with their high refractive index, have a disadvantage resulting from their light-guiding effect that prevents a large fraction of the luminescence generated inside the film from escaping. This light-trapping effect decreases the external luminescence efficiency, usually by a factor of 1.5~1' to 2nZ (where n is the refractive index of the film; Goldberg, 1966),compared with a powder screen of the same chemical composition. For most phosphor materials, whose refractive index is about 2, this factor is in the range of 5 to 10. Since the light emerges from the film most efficiently at imperfections, this may result in a nonuniformity in screen brightness. In order to reduce the effect of the light trapping, modifications of the film geometry have been proposed, such as formation of a rough surface, producing minute

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cracks, or dividing the film into a mosaic of islands (Huo and Huo, 1986). Under favorable conditions, the external efficiency can be increased somewhat by these methods with minimum sacrifice of the advantages 1 and 2 indicated above.

2. Brief Review of Thin-Film CRTs a. High-Contrast. High-Resolution C R Ts For displays that require high resolution and high contrast in very bright ambient conditions, e.g., a projection-type head-up display in an airplane cockpit, a penetration tube (see Section VILA) having overlaid green- and red-emitting films on a glass faceplate has been commercialized by Thomson C . S. F. This can produce a trace down to 0.2 mm in width. To make the color changes more distinctive with changes in beam voltage, the dead voltage (see Section 1II.B) of the second (green-emitting) layer was increased to 10 kV by means of a transparent barrier layer deposited between the two films. Another penetration tube, developed by Sauerborn et a/. (1983), has a structure such as shown in Fig. 28. The luminescent screens here are deposited on a sapphire substrate and coated with a thin black layer (easily penetrated by the electron beam) for contrast enhancement. The black layer has a graded composition of V-V20, ( V 2 0 , at the phosphor surface), resulting in a graded refractive index that reduces optical reflection of ambient light at the interface with the phosphor. Similarly, to enhance the contrast, Young et al. (1986) developed a siliconoxygen black layer, varying in oxygen content, to produce a graded refractive index that matched a red-emitting Y 20,: Eu film phosphor deposited on sapphire. Without the silicon-oxygen layer, the phosphor film had a contrast ratio comparable with that of a settled powder screen. However, the addition of the black layer increased the contrast ratio by a factor of 2.5.

BLACK LAYER

SA PPHI R< n = 1. 76

n- 2 . 2 2

FIG. 28. An example of a penetration tube with thin-film screens. This tube has red-emitting La,O,S: Eu3' and green-emitting La,0,S:Tb3+ in adouble layer with thicknesses of 200nm and 126 nm, respectively. They are backed with a black layer having a graded composition of V,O, - V to increase contrast (Sauerborn et al., 1983).

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The investigation by Young et al. (1986) provides a means of comparing the transparent film phosphor with a settled powder screen in terms of brightness and contrast. Their Y,O, : Eu thin films without a black coating had an external efficiency of 2 Im/W, while the best available Y,O,:Eu powder phosphor has an efficiency as high as 17 Im/W. The reflectance of their black silicon-oxygen film ranges from 1 to 2%, while the diffuse reflectance of the settled Y,O,:Eu powder is about 80 to 85% in the visible region. Using the following equation, originally given by Uehara et al. (1987) for color picture tubes with a black matrix, we can calculate the contrast C : C=1

+ ( 4 n B T ) / ( L R+ L ( l - R ) R , T 2 ) ,

(21)

where B is the screen brightness, L the ambient illuminance, T the transmittance of the faceplate, R the reflectance of the faceplate surface and R , the reflectance of the powder phosphor layer or a backing layer such as a contrast-enhancing black layer. Let us suppose that we can take R , = 0.8-0.9 for the powder phosphor layer and R x 0.1.Using this relation, one finds that an optical filter (or a dark-tint faceplate) with 10 to 20% transmittance increases the contrast of the powder screen to a level as high as that of the phosphor film coated with the black layer for any finite value of L . (For T = 0.1-0.2, L ( l - R ) R , T 2 << L R , while with the black backing layer, we can take R , z 0. For either case, therefore, we find C z 1 + (47cBT)/LR.) Under these conditions, the external efficiency of the powder screen is decreased to a level of 1.7 to 3.4 Im/W, which is still higher than that of the blackcoated film, i.e., 1 Im/W. The above consideration indicates that the feature most important for the transparent film is not the contrast obtainable but the high resolution, which is estimated to be about 250 line-pairs/mm, about 10 times larger than for the settled powder screen. 6. High-Luminance, High-Resolution CRTs In other applications, there is an increasing demand for higher current loading in tubes, to obtain higher brightness in projection systems. With respect to phosphor materials, there are mainly two factors that limit this brightness. One is the temporary drop in luminescence efficiency with an increase in temperature (see Section II), while the other is a more permanent aging or burning of the phosphor enhanced by heat (see Section VIII). Thin-film screens can minimize both of these effects, since they have good thermal contact with the substrate. Also, the deposition of the films naturally does not involve a wet process, which sometimes deteriorates the phosphor surface and causes aging (see Section VIII). One of the best thin-film phosphor materials for use in tubes with high electron-beam power is Y,AI,Ol2 (YAG). This is the host material of a greenemitting phosphor powder, P53, and of some lasers as well. Its thermal

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conductivity is about a hundred times larger than that of glass; it is chemically stable and also has a high melting point, making it resistant to aging. In addition, crystal growth of YAG and related compounds benefits from the abundant knowledge and technology accumulated in the development of bubble memory devices. Robertson et al. (1980) demonstrated the feasibility of using a singlecrystal screen of rare-earth-activated YAG. They fabricated tubes having a two-inch-diameter YAG wafer as a faceplate on which the luminescent film was epitaxially grown. Using Ce3+ as an activator, which has a very short emission lifetime (nanoseconds), good linearity of light output (i.e., without saturation) was found as a function of input power up to 10 W/cm2. When scanned with an interlaced field of 575 active lines and 25-Hz repetition frequency using a beam spot of 9 pm diameter (e- value) and a 12 x 16 mm raster area, the tube could handle up to 20 W of beam power (equivalent to 10 W/cm2) when properly cooled. In comparison, conventional projection tubes can handle only a few watts per square centimeter. Operated at higher beam power and lower resolution, the tube is capable of a maximum luminance of 64,000 cd/m2. Thus, it may also be used, for example, as a light source for a copying machine or a light pen in a data-input interface. Recently, a tricolor luminescent screen two inches in diameter with a stripe pattern was fabricated for use in a single-tube projection system (Huo and Huo, 1985).The red, green and blue components were prepared by doping of the YAG with Eu3+,Ce3+ and Tm3+,respectively, using photolithography (see Fig. 29). Each color stripe was 37 pm in width with a pitch of 120 pm for the color triplets.

’

PLASMA ETCH

I

PLASMA ETCH

YAG

FIG. 29. Schematic diagram of the stripe-etching process for manufacturing tricolor cathodoluminescent epitaxial films. The red, green and blue components are Y,A1,0,, (YAG) doped with Eu”, Tb” and Tm”, respectively grown on an undoped YAG substrate. [After Huo and Huo, 1985. 0 1985 IEEE.]

2

9.

FIG. 30. (a) A schematic isometric view of a one-dimensional array of light-emitters. 1, element of the array; 2, a substrate serving as a heat sink; 3, metal coating; 4,dielectric coating; 5 , light-emitting core; 6, electron beam; and 7, electron gun. (b) Schematic view of a CRT employing a onedimensional array of light emitters. 8, tube envelope; 9. electron-gun; 10, electron beam; 11, the onedimensional array; 12, output coupling window; 13, direction of the electron-beam scan. The electron beam deflection and focusing means are not shown for simplicity. [After Shmulovich and Berkstresser, 1985.1

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES

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A one-dimensional array of YAG:Ce has been proposed by Shmulovich (1984), consisting of a row of elongated phosphor film elements (see Fig. 30) mounted on a heat sink. Each luminescent element of the layer has a reflective coating on both surfaces, causing the luminescence to emerge with high intensity from one end of the element. The linear array itself, used as the faceplate of a CRT, is irradiated by a scanning electron beam whose oblong cross-section covers the entire area of an element. This arrangement takes advantage of the inexpensive scanning capability of the electron beam and may be suitable for applications such as printing, optical addressing of a memory medium and communication. c. Electron-Beam-Pumped Lasers Electron-beam pumping can provide a high power density, can allow scanning of the surface and can be applied to almost any material. It is, therefore, an attractive means of laser pumping, particularly in cases where alternative means are not available. For more than 20 years many investigations have been carried out on electron-beam-pumped single crystals of 11-VI compounds (much below room temperature) with the aim of producing a visible-light semiconductor laser. One of the early achievements in this area was the demonstration of a 12 m2 color display using projection tubes with cooled laser systems (Basov et al., 1975). An advantage of such systems, aside from their high brightness, is the fact that the emitted light is directional, reducing the diameter of the projection lens. In recent work other films 20 to 30pm in thickness were lased at room temperature. The materials used and their characteristics are given by Colak et al. ( I 985). The threshold current density of such systems is expected to be reduced by better crystalline quality and decreased number of undesirable impurities and defects. However, a better approach for reducing the threshold results from adding other layers with a higher band-gap and a lower refractive index on both sides of the luminescent layer to form a double heterostructure that confines the light and the electrons in the luminescent (or active) layer. Recently, a miniature CRT using GaAs/(Ga, A1)As heterojunctions was shown to lase at room temperature (Levy et al., 1984). Although a CRT screen composed of YAG material itself would probably work as a laser, Shmulovich (1984) has proposed making use of the incoherent radiation of a YAG film screen as a pumping source for other materials. Such two-step pumping of a ruby (AI20,:Cr3+)film coupled to a YAG:Ce3+ film could be up to five times more efficient than pumping by flashlamps.

3. Preparation Techniques f o r Thin Films The recent activities described above have profited greatly from progress in the preparation techniques of thin films, some examples of which are reviewed below.

348

TAKASHI HASE et cl.

The deposition of Y,O,:Eu on sapphire has been accomplished by R F magnetron sputtering of mixed oxides (Y,O, and E u 2 0 3 ) at a substrate temperature of 350°C. As deposited, the film has poor crystallinity and does not exhibit the normal luminescence spectrum. By thermal annealing at IOOO'C, however, the crystallinity and the efficiency are improved and the emission characteristic of the material is obtained. The measured efficiency without a black layer is 2 Im/W. Since a volatile element may reevaporate during the film formation resulting in serious deviation from the correct stoichiometry, it is desirable to supply an additional amount of this volatile element during deposition. The quality of La,02S films, for example, can be improved by adding H2S to the sputtering gas (Ar), and then annealing in a reducing atmosphere of Hz and SO,. The external efficiency of La,O,S:Eu films prepared in this way is 1 Im/W, which is one-third of the efficiency of powder phosphors. The 11-VI compounds are usually deposited by electron-beam evaporation or sputtering. The techniques for these materials have been well developed, particularly for ZnS doped with Mn or a rare-earth ion, in connection with their use in electroluminescent panels. Films of YAG and related materials can be grown by the liquid phase epitaxy developed for the growth of iron garnets. The melt contains a flux, usually PbO and B,O,, in addition to oxides of constituent cations (Robertson ef al., 1980). Another modern technique for film preparation is to make use of laser radiation for heating. This has the advantage of allowing the phosphors to be heated without raising the substrate temperature too high. For example, annealing by a CO, laser enhanced grain growth and improved the efficiency of YF, deposited on a glass substrate (Trimmier and Knutsen, 1981). Laserassisted melt growth was used for Zn,SiO,:Mn'+, (Chang et al., 1980), CaW0,:Nd and YAG:Nd (Grabmaier et al., 1973). To incorporate Tb into a YAG film, Robbins et al. (1982) showed that ion implantation could be used. Many semiconductor devices developed recently are designed to have precisely controlled device structures and chemical compositions. For example, the precise film growth techniques developed for producing superlattice structures could possibly be used to create new types of cathodoluminescent devices. These new techniques involve molecular beam epitaxy (MBE), organometallic vapor phase epitaxy (OMVPE) (or metallorganic chemical vapor deposition (MOCVD)), atomic layer epitaxy (ALE) and chemical beam epitaxy (CBE). The reader can consult reviews by Parker (1985) on MBE or CBE and by Ludowise (1985) on OMVPE. The conference proceedings on OMVPE (Watanabe et al., 1988) may be also helpful for obtaining state-ofthe-art information.

PHOSPHOR MATERIALS FOR CATHODE-RAY T U B E S

349

A . Background

During the course of CRT operation, bombarded areas of the phosphor screen tend to become more or less darkened and degraded in efficiency, with the aged portion usually turning brown or black, as if it were charred. This phenomenon is called “burning” when it occurs within a short time and “aging” when it occurs over a long period. Hereafter, we call both processes “aging” for the sake of simplicity, unless the two need to be distinguished. When a phosphor-coated faceplate glass is exposed to the electron beam, coloration of the glass also occurs in addition to aging of the phosphor. This phenomenon, called “browning”, is described separately below. Aging is not a new problem, but it has become more and more serious with the increasing demand for high current-density operation required in applications such as projection-type television, cockpit displays and computer terminal displays. In many cases, the darkening can be thermally bleached by annealing the phosphor at several hundred degrees Celsius, or even by leaving it at room temperature for many days. From such observations, one can speculate that the darkening originates from the generation of many kinds of complex color centers. The atomic arrangements corresponding to the color centers are, however, not known at present. To a first order, it is observed that the aging can be correlated with the total amount of charge per unit area falling on the phosphor. For many commercial phosphors, Pfahnl(198 1) and Infante (1 985) have given half-lives of brightness in terms of the total charges deposited on a unit area in coulomb/cm2, as indicated in Table V. The most durable phosphor in this list is P53 (Y3Al,0,, :Tb). At the standard operating conditions of a projection tube, i.e., a beam current of 0.5 mA, a spot size of 0.3 mm and a raster area of five inches diagonal, a half-life of 100 coulomb/cm2 corresponds to an operating time of 1700 hours. If the scanning is stopped, producing a stationary spot, the same amount of aging occurs after only 30 seconds of operation. In color picture tubes, the spot size is about 1 to 2 mm, and the raster area has a diagonal that ranges from 14 to 37 inches. The operating time in this case, corresponding to the effective life, is two orders of magnitude longer than for the projection tubes. The total charge deposited per unit phosphor area, however, is not the only factor controlling the aging. For example, in the case of InB0,:Tb l9

By H . Yamamoto

350

TAKASHI HASE et a/. TABLE V

PHOSPHOR AGINGAS MEASURED BY THE HALF-LIFE (LIFETO 50% OF INITIAL BRIGHTNESS)IN TERMS OF THE INTEGRATED ELECTRIC CHARGE REACHING THE PHOSPHOR WTDS

JEDEC

Chemical formula

Half-life“ (coulomb/cm2)

GJ GR

P1 P39 P22 (G) P55 (P22B) P4 P43 P26 P53 P46 P47 P16 P56 (P22R-Oxide)

Zn,SiO,:Mn Zn,SiO,:Mn, As ZnS:Cu, Al ZnS : Ag, CI ZnS:Ag, CI + (Zn,Cd)S:Cu, Al Gd,O,S:Tb ZnF,:Mn Y,AI,O,,:Tb Y,AI,O,,:Ce Y,SiO, :Ce Ca,MgSi,O, :Ce Y,O,:Eu

> 100.0 > 25.0 35.0 35.0 35.0 > 100.0 0.2 200.0 > 100.0 > 100.0 0.2 IOO.0

X X

ww GY

KJ KG BH RF

a The data cited by Infante (1985) were supplied by P. Seats. No comments were given regarding the effect of glass browning on these data.

(Matsukiyo et al., 1986), a higher current density induces faster aging even with the same total charge deposited. At the low anode voltages used in vacuum fluorescent displays (below 50 V), the half-life of ZnO expressed in coulombs is about 100 times longer than that of the same material at high voltages (20 kV), (Kazan, 1985). We describe below some factors related to the aging of phosphor materials.

B. Factors Involved in Aging Klaassen et al. (1987) analyzed the degradation of three phosphors and found a different reason for the degradation in each material: namely, the formation of color centers in alkaline earth aluminate doped with Eu”, the formation of a nonluminescent layer on the surface in Zn,SiO,: Mn2+ (Pl), and a decrease in the concentration of luminescent Ce3+ ions in Y,SiO,: Ce3+. In the case of Zn,Si0,:Mn2+,,desorption of oxygen by electron irradiation was reported (Hurd, 1974). This unique property of the surface layer of P1 may be related to a rapid drop (typically 20 to 30%) in the efficiency observed when the electron beam initially radiates this phosphor. Sometimes during the initial operation period, an increase in brightness, customarily called “white burning”, is first observed. From the point of view of the bulk properties of a phosphor, favorable

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES

35 1

conditions are, above all, strong chemical bonding and a tightly packed ion arrangement, which forbids ion migration. Impurities that produce vacancies in a lattice also cause aging. For example, in oxides aging can proceed rapidly as a result of the presence of F- ions introduced from a flux during synthesis. The formation of color centers by electron bombardment has been throughly studied for alkali halides, alkaline earth fluorides and some binary oxides (Itoh, 1982). The type of color center best understood is an associated pair of an F- and H-center, i.e., a Frenkel pair. The fundamental knowledge obtained on these materials may also provide suggestions regarding the atomic configurations involved in phosphor aging, despite the difference in the chemical compositions and the temperatures involved. Yamamoto et a!. (1985) suggested that the aging can be accelerated by the hydrolysis and subsequent chemical reaction of the phosphors with the potassium silicate employed as a binder during deposition of the screen. The aging of hygroscopic materials, such as CaS phosphors, may thus be suppressed by control of the pH of the screening solutions, which reduces the hydrolysis. Most CRT manufacturers probably know that a phosphor screen covered with a large amount of silica gel formed from the potassium silicate tends to age rapidly. The amorphous silica on the phosphor surface, when present in excess, makes the phosphor layer loosely packed and as a consequence prevents heat dissipation. This was actually observed by Yamamoto et al. (1987) in thz case of InB03:Tb3+,which suffers from aging more rapidly with an increased surface temperature. They demonstrated that the packing of the phosphor grains, as well as the intrinsic thermal conductivity of the bulk material, can play an important role in the aging rate. They also found that coloration of the silica by electron bombardment is too weak to be the main cause of the aging. In short, the following early statement by Leverenz (1950) still points out the essentials: “The harder, higher-melting, water-insoluble materials are the most resistant to loss of luminescence during operation.” C . Browning of Gluss As mentioned above, the faceplate glass turns brown when exposed to high-energy electrons. There are two reasons for the browning: irradiation by X-rays generated in the glass (and shadow-mask in color tubes), and the direct effect of the electrons entering the glass. As expected, the browning of the glass is increased when the phosphor screen has many pinholes, but in commercial tubes with a controlled screen weight, the loss in brightness by glass browning is much less (about loo/, at worst) than that caused by phosphor aging.

352

TAKASHI HASE et al. I

0 I --O-Si-O-MM'

I 0

h3

I

0

I -0-Sit I

9

,'-a, 0 ;tM'+e '.-/'

I FIG.31. Color center formation processes proposed for a silicate glass (see, for example, Yokota, 1954).

As a result of extensive studies of the coloration by X-rays, the atomic structures of the resulting color centers in glass have been clarified. For any glass composition, color-center formation is initiated by liberation of an electron from (or, in other words, trapping of a hole by) an 0'- ion by ionizing radiation. This process is schematically shown in Fig. 31 for a silicate glass. When the liberated electron is trapped by an oxygen vacancy neighboring an alkali ion, it results in visible absorption bands. The absorption wavelengths depend on the alkali ion species. For Na the bands are found around 450 and 620 nm. When a hole is bound around an alkaline ion vacancy, it results in an ultraviolet absorption band at 300 nm, the energy of which is independent of the ion species (Yokota, 1954). It is found that the visible absorption can be suppressed by the addition of CeO, as a dopant to the glass. It is believed that Ce3+ works as a powerful recombination center by trapping a hole and then an electron in succession (Levy, 1960).By this action, electrons and holes generated by the radiation are prevented from reaching the vacancies that would otherwise cause the color centers. (However, an ultraviolet absorption from the Ce3+ itself appears.) In practice, therefore, the faceplate glasses of CRTs usually contain 0.1 to 0.2 atomic percent Ce. In the case of bombardment by electrons, these have the effect of reducing alkali and impurity ions. This results in the formation of very fine grains of alkali metals, which are the main reason for the glass browning (Ishiyama et al., 1975). In fact the browning is increased with increasing content of alkali ions. The effect is particularly strong in glasses containing K,O, compared with Na,O or Li,O (Ishiyama et al., 1975).The incorporation of CeO,, which is quite effective in reducing X-ray browning, does not help much to decrease the electron browning. During the course of electron bombardment, mobile ions, e.g. Na', migrate towards the inside of the sample, with the maximum Na concentration appearing at a depth comparable with the electron range where a negatively charged layer is formed (Battaglin et al., 1982).Accompanying Na

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES

353

migration, oxygen depletion is observed. The phenomenon is explained by the following reactions (Lineweaver, 1963; Puglisi et al., 1983):

-,-Si-Si + to,

-Si-O-Si-Si-0-Na' -Si+

+ 02-+ Na' + -Si-0-Si+ Na'.

+ -Sif

+ 'Na-0-Si-

(22) (23) (24)

The browning produced by either X-rays or electron bombardment can be thermally or optically bleached more readily than the reversal of phosphor aging. Rengan et al. (1985) analyzed radiation damage in commercial glass used for projection CRTs. They found, in addition to color center formation, evolution of oxygen gas and a depletion of Sr, Na and K ions from the glass surface, similar to the processes described above, as well as thermal bleaching,

Ix.CONTRAST-ENHANCING TECHNIQUES IN COLOR TUBES 2o As is well known, the contrast of an image viewed on a phosphor screen may be seriously degraded by ambient light. Fig. 32 shows a schematic CRT face plate

T

-_-_- -----__

I

---

~

-

_ . __ - _ -_ --.

FIG.32. Cross-section of color display tube screen showing ambient light reflection. L is the illuminance of the ambient light, B the brightness of the phosphor screen, P the pitch of a set of RGB phosphor stripes, and C the stripe width of the black matrix window.

zo

By T. Hase

354

TAKASHI HASE et al.

diagram of the faceplate of a shadow-mask color cathode-ray tube. In addition to the phosphor brightness B and ambient illuminance L , the specularly reflected light at the faceplate surface and the diffusely reflected light from the phosphor screen are shown. The contrast, C, defined as follows: C=

+

Total reflection brightness Luminescent brightness Total reflection brightness

where B is the brightness of the phosphor screen, R , the diffuse reflectivity of the phosphor screen, R the reflectivity of the glass panel front surface, T the transmittance of the panel glass, L the illuminance of the ambient light, t the stripe width of the black matrix window and P the pitch of a set of color phosphor stripes (Uehara et al., 1978). As indicated by the formula, reduction of the diffuse reflection from the phosphor is effective in improving the contrast. With respect to the faceplate glass, contrast can be improved by a decrease in the transmittance of the glass and also by a surface treatment that reduces the specular reflection. For reducing the reflection from the phosphor screen the “black matrix” and “phosphor pigmentation” methods have been developed. We describe these methods in greater detail below. A. Nonglare Glasses As mentioned, one method for increasing the contrast is to reduce the transmittance of the glass faceplate. For example, the clear panel glass (transmittance of 8 5 % ) can be replaced with gray (63-73% transmittance), tint (57%) or dark tint (46%)glass with a corresponding sacrifice in brightness. A more refined approach is to use glass doped with Nd3+ ions whose main absorption lines are located at around 580 nm, between the red and green emission bands. The glass, therefore, can cut down the reflected light in this specific wavelength region with only a little decrease in the overall emission output. One can wash out an image of the light reflected from the glass surface by making the light more scattered rather than specular (directional). To scatter the light, the glass surface can be made rough by chemical etching (Ishii et al., 1983), or it can be coated with a scattering layer of silica, a plastic film or a plastic mesh. In some cases the outer surface of the glass is coated with an antireflection

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES

355

film produced by evaporation. Although this is very effective in reducing specular reflection, it is not used often because of its high cost and the need to keep the surface very clean.

B. Black-Mutrix Screen

This “black-matrix’’ method developed in 1969 makes use of black material, specifically graphite, which is deposited in the regions between the phosphor dots or stripes. This “black matrix” is formed by photolithography, before the pattern of phosphor dots or stripe is deposited. In tube operation the “black matrix” areas are shielded by the shadow mask and not bombarded by the electron beams, thus producing little loss in brightness. Since the “black matrix” reduces the reflection of ambient light by a substantial amount, the contrast can be made more than twice as high as that of a screen without the black matrix (Fiore and Kaplan, 1964, 1969). C. Pigmented Phosphors

In this approach a suitable color filter is provided for each color phosphor element. This filter is transparent to the emitted light of the phosphor but absorbs light of other wavelengths. In an early approach (Kaplan, 1967), a mosaic of filter elements of particles was settled on the faceplate before the phosphors were deposited. This method has not been used in practice because of the complications involved in processing. In a later method (Lipp, 1975), tiny particles of a red pigment Cd(S,Se), were attached to the surface of each red-emitting Y,O,S: Eu phosphor grain. At present, however, ferric oxide is widely used as the red filter instead of Cd(S,Se) because of the toxicity of Cd. Similarly, particles of a blue pigment, (ultramarine) are attached CoO.nAl,O, (marine blue) or Na,AI,Si,O,,-S, to the ZnS:Ag blue particles. In general, no pigment is used for the green phosphor because of the yellowish body color of ZnS:Cu or ZnS:Cu, Au, Al. The pigment particles themselves are very small, their average size being less than 1 pm. This should be compared with the phosphor grains whose size is about 4-8 pm. Usually, the pigments cover less than about 20% of the phosphor surface area, but, by virtue of light scattering in the particle layer and the large absorbance of the pigments, much of the undesirable ambient light is effectively absorbed. Many methods have been devised to coat the phosphor particles with pigment. A typical method disclosed by Lipp (1975) is described below.

356

TAKASHI HASE et a/.

The pigment particles, dispersed in a solution of a water-soluble resin such as polyvinyl pyrrolidone, are mixed with a phosphor dispersed in an aqueous solution of gelatin. The resulting mixture is stirred and the resultant precipitates formed are dried to obtain the pigment-coated phosphor. In the preparation of a pigment-coated phosphor, it is important that the pigment particles be uniformly and strongly adhered to the phosphor surface. Desired methods for uniformly and strongly adhering the pigment particles to the surface of the phosphor include an electrostatic coupling method, a suspension polymerization method, a copolymerization method, and a method using a mixture of gelatin and 0.01-0.2 wt % of gum arabic as an adhesive (Kanda et al., 1979). Details on these processes are given by Uehara et al. (1978), Ikegaki et al. (1976) and Kotera et al. (1981).

X. CONCLUSION^^ The highly advanced state of development of CRTs used for consumer, military and industrial applications has largely been made possible by the advances in phosphor materials. However, to further improve CRT performance, research is continuing in a number of directions to develop materials with reduced brightness saturation, special color characteristics, longer life and greater ruggedness, and special persistence characteristics (such as for the reduction of flicker). Above all, high luminescence efficiency, which has always been the most indispensable requisite, is now more urgently called for than before by the recent trend toward brighter, larger screen images with higher resolution. As indicated in Section 111, however, the energy efficiencies of commercial TV phosphors (ZnS:Ag, CI, ZnS:Cu, Al and Y202S:Eu3+) are quite close to the theoretically predicted values. It seems, therefore, difficult to significantly improve the efficiencies of these phosphors (e.g., by more than lo%), although small increases may be made possible by a combination of technologies to control lattice defects and to optimize the structure of the phosphor screen. Many attempts to discover new TV phosphors have been made, mainly in the area of rare-earth activated oxides, oxyhalides, oxysulfides and sulfides, but with little success. There is some opinion that the next step might be a survey of non-oxides such as nitrides and phosphides (Lehmann, 1987). Not many of these materials have been reported as phosphors, although insulatH.Yamamoto

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES

357

ing or semiconducting members, e.g. BN, GaN, ScN and BP, are known to show luminescence. However, many difficulties remain to be overcome, such as growth techniques of grains as large as several microns and incorporation of efficient luminescent centers. Compared with the usual (direct-view) color picture tubes, projection-type tubes provide a greater incentive to find new phosphors, since conventional TV phosphors cannot maintain their efficiencies under the loading power of projection tubes, which is about two orders of magnitude higher than that of direct-view tubes. For this purpose, green-emitting ZnS:Cu, Al and its modifications have been replaced by Tb-activated oxides or oxyhalides, which show much less brightness saturation and greater ruggedness even under high current density. At present the central issue is the development of a blue phosphor that can substitute for ZnS:Ag, Al or ZnS:Ag, CI materials whose brightness saturation presents a serious problem under high loading power. For this purpose exploratory work on rare-earth phosphors as well as improving ZnS:Ag phosphors is necessary. However, for the improvement of efficiency (including the reduction of saturation), an understanding of nonradiative processes is not sufficient at present. Perhaps analysis of the classical ZnS phosphors in the light of modern technologies will still provide fruitful results. Increasing loading power has also made the aging problem much more serious than before. Chemically stable materials having a high melting point and a high bulk thermal conductivity are important as hosts for high-loading phosphors. In this respect rare-earth oxides form a promising class of materials, as represented by Y,O, and Y,AI,O,,. It has also been shown that aging can be reduced by surface-chemical methods, including optimization of post-treatment or deposition processes. Possibly, incremental developments in this field will result in a large improvement. The requirement for long-persistence phosphors (in the range of several tens of milliseconds) imposes a severe restriction on the luminescent center that can be used. This is indicated by the fact that the strongly forbidden transition of Mn2+ provides almost the only useful luminescence for this purpose. However, it seems difficult to meet other requirements, i.e., efficiency, color and life, with the limited group of materials using such luminescent centers. From the point of view of material scientists, it would be desirable to reduce persistence requirements to a level of several to ten milliseconds, since this will allow many new materials to qualify as possible phosphors. Perhaps this will be brought about by a several-fold increase in the electron beam scanning rate. Concerning phosphors for vacuum fluorescent displays (VFDs), efficiencies have been greatly improved in the last four or five years (see Section 1V.F). Even Z n 0 : Z n and (Zn,Cd)S:Ag ,Cl, which have a long history,

358

TAKASHI HASE ec al.

have been significantly improved for this application. Compared to TV phosphors, there seems to be more room remaining for improvement of the VFD phosphors, since the progress so far made has been limited to an investigation of basic material factors, such as reduction of impurities and dislocations. The problem here again is the poor efficiency of blue-emitting phosphors, which have shown least progress. It is to be hoped that a new efficient material with reasonably low electrical conductivity will be developed that can replace the conventional ZnS:Zn (or Zn-treated ZnS). Almost all CRTs use phosphor materials in powder form because of their high efficiency and ease of screen fabrication. However, an interest in thin-film phosphors has been revived recently, since their advantages of very high resolution, high contrast and high loading capability meet the increasing demands for higher picture quality. The largest problem that hampers widespread application of thin-film phosphors is their poor external light output, caused by refractive trapping of the luminescence. When a practical way to fabricate structured layers with a reasonable compromise between light output and resolution is devised, thin-film phosphors may find important areas of application particularly in computer terminals. Until now most of the successes achieved in phosphor development have resulted from experimental work rather than theoretical predictions., However, theoretical understanding of the physics of phosphors has been quite useful in providing insight and guidance on what should be tried and what should not. In the mature stage of material development of cathode-ray phosphors, theoretical and analytical investigations will be of increasing importance if breakthroughs are to occur in this technology.

ACKNOWLEDGMENT The authors express their sincere gratitude to Dr. B. Kazan for his invaluable editorial guidance in preparing the manuscript and his help in improving the English.

APPENDIX 1

CHARACTERISTICS OF WIDELY USEDPHOSPHORS FOR MAIN CATEGORIES OF CATHODE-RAY TUBFS COLORPICTURE TUBES Color point" Chemical composition ZnS :Ag (pigmented) ZnS:Cu, Al ZnS:Au, Cu, AI (ZnCd)S:Cu,Al Y,O,S:Eu (pigmented) YV0,:Eu

Emission color"

Emission peak (nm)'

x

y

blue yellowish green yellowish green yellowish green red red

450 530 535 530 626 619

0.146 0.282 0.306 0.321 0.640 0.664

0.061 0.620 0.602 0.613 0.352 0.331

Lumen Decay time".b equivalent" (10%) (WW) S S S S M M

140 494 483 509 215 217

Energy efficiencyd Designation Designation (%I EIA' WTDS' 21 17.23 16 17 13 7.1

Relative brightness (0;)"

P22 P22 P22 P22 P22 P22

X X X X X X

50 190 185 192 65 30

P4

ww

115

P3 1 P39 P27

GH GR RE

P46 P4 7

KG BH

180 94 23 30 32 20

-

-

-

P45

WB

79

-

-

~

BLACKAND WHITEPICTURE TUBES

w \o IZI

ZnS:Ag+(ZnCd)S:Cu, Al

white

450 560

0.267 0.291

S

TUBES TERMINAL DISPLAY ZnS:Cu Zn,SiO,:Mn, As y-Zn3(POJ2:Mn ZnS: Ag, Ga. CI Y ,AI,O,,:Ce Y,SiO,:Ce Y A10,: Ce Y ,O,S: Tb -+

Cd,(PO,),CI:Mn

green green red blue greenish yellow bluish violet ultra violet white orange

530 525 636 450 535 410 370 418 544 590

0.265 0.205 0.655 0.147 0.402 0.169 0.231

0.558 0.714 0.343 0.052 0.557 0.109 ~

0.246

S L L L

vs vs vs M

23 163

6.7

-

514 74

~

0.558 0.440

L

LA

79

APPENDIX I (Continued) PROJECTION TUBES Y,O,: Eu Zn,SiO,: Mn Gd,O,S :Tb Y,AI,O,, :Tb Y,SiO, :Tb ZnS:Ag, Al

red green yellowish green yellowish green yellowish green blue

611 525 544 544 544

0.642 0.205 0.334 0.342 0.340 0.149

0.351 0.714 0.561 0.572 0.570 0.051

M M M M M S

284 520 478

8.7 8 15

P56 P1 P43 P53 ~

~

RF GJ GY KJ ~

-

64 100 138 92 115 50

VACUUM FLUORESCENT DISPLAY TUBES

’

ZnO :Zn ZnS:Zn +In,O, ZnS:Au, Al+ In,O, (ZnCd)S:Ag +In,O,

greenish white blue yellow red

505 460 555 650

0.246 0.146 0.353 0.640

0.419 0.160 0.578 0.358

vs S S S

a Spectral curves, emission color, emission peak, color point, decay time and relative brightness were measured by Kasei Optonix, Ltd. These measurements were made by demountable apparatus with light output from the same side as the incident electron beam. Specimens were prepared by the sedimentation method. Assumed test conditions are for 20 kV electrons with a continuous beam of lpA/cmZ current density. Relative brightness standard is P1 phosphor. By definition, relative brightness = a constant x lumen equivalent x energy efficiency. The data in the table are not necessarily consistent, having been obtained from different data sources. Decay time measured from 100%to 10%emission level. Assumed test conditions are for 12 kV electrons with a continuous beam of 0.3 pA/cm2current density. VS (very short), less than 1 ps; S (short), 1 ps-1 ms; M (medium), 1-30 ms: L (long), 30 ms-1 s. Lumen equivalent is the number of lumens contained in one watt of radiation of the given spectral distribution. See Kano, et al. (1982),Yamamoto (1984), Ludwig and Kingsley (1970),and Kingsley and Ludwig (1970). Energy efficiency is defined as the ratio of the energy of the radiation emitted to the energy of the incident electrons. Data are somewhat scattered depending on publications. See Alig and Bloom, (1977),Kano et a!. (1982)and Yamamoto, (1984). ‘The Joint Electron Device Engineering Council (JEDEC) “ P number phosphor designation system has been in use in the United States since 1945. The Worldwide Phosphor Type Designation System (WTDS) was adopted to replace several existing phosphor designation systems previously in use in various countries, including the JEDEC “ P number system. Principal advantages of the WTDS system include international recognition and indication of the phosphor color through the first letter of the two-letter code (Keller, 1983). All new phosphor registrations will be assigned by the Electronic Industries Association (EIA) JT-3 1 Committee on Optical Characteristics of Display Devices. The details of the system are also described in TEPAC Publication No. 116-A (1985).

36 1

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES

APPENDIX 2 RELATIVE SPECTRAL DISTRIBUTION CLIRVES OF CATHODOLUMINKCENCE FOR THE PHOSPHORS LISTED I N APPENDIX 1

EMISSION

/I I

x

I 1 I

500

600

700

ZnS : Au, Cu, A1 100

50

400

500

600

700

800

e

400

APPENDIX 7 ( C o n t i r i i c c , ~ )

800

362

TAKASHI HASE et al.

APPENDIX 2 (Continued)

100

50

400

580

600

700 Wavelength ( n m )

800

0 400

500

600

Z n S : Ag t ( Z n C d ) S : Cu, AL

100

700

800

Wavelength ( n m )

Z n S : Cu

50

E 400

500

600

700

800

400

500

600

708

800

Y3AL5OI2:Ce

400

500

600

780

800

400

500

600

700

800

363

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES

Y, SiOJ :Ce

100

58

400

400

500 600 700 880 Wavelength (nm)

500 600 780 Wavelength ( nm 1

800

EU

Y203 :

400

500

600

700

800

Zn2Si04: Mn

400

580

600

700

800

400

500

600

700

800

100

50

400

500

600

700

800

e

TAKASHI HASE et ul.

364

APPENDIX 2 (Continued)

ZnS : Ag, A1

100

50

50

0

Z n O : Zn

100

U I n I I I I I A I I U I I I I 400

500

600

700

Wavelength (nm)

I /I

0 800

400

1

500

I

1\1

600

I 700

Wavelength (nm 1

I

800

365

PHOSPHOR MATERIALS FOR CATHODE-RAY TUBES

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Index

A

Accelerometer, 25 1 Acetone, 238-239 Activator, 274, 278 Adsorption, 245-246 AFM. See Atomic force microscopy Aftergrow, 285 Ag, 2 1I - 2 12,242,245 246,25 1 Ag( 100).21 1,242 Ag(llO),211 Al(11 I), 213 Al( 1 1I ) - 0 , 213 AI,,Mn,,, 216 AI,O,, 237-238 AI,O,:Cr”+, 347 Amino acids, 239 Applications of STM, 203-246 biological materials, 238-240 dynamical processes, 245-246 insulators, 236-238 layered materials, 230-234 magnetic materials, 240-241 metals, 204-216 nanotechnology, 241 -244 organic molecules, 238-240 semiconductors, 216- 230 superconductors, 234-236 surface modification, 241 -244 Asperities, 84-85, 88, 95, 97 Atomically clean surface, 106 Atomic force microscopy (AFM), 25 1-255 Au, 209,238,242-243.251 Au( 100). 207-208 Au( 110). 205-207 Au( 11I), 204-205,245-246.249 A ~ ( l l l ) - P b 246 , Au-GaAs(lCO), 249 Auger electron spectroscopy (AES), combined with STM, 163 Auger process, 285 AuPd, 249 Au-Si(100), 249 -

B Bacteriophage, 239 Ballistic-electron emission spectroscopy (BEEM), 249 Band bending, 216-217,237 Band gap, 216-217,236-237 Barrier-height, 157-159, 160-163 Barrier-height profiling, 160- 163 Beam-index tube, 317 BEEM. See Ballistic-electron emission spectroscopy Bethe’s formula, 295 Bimorph, for fine displacement, 169-1 70 Biological materials, 238-240, 253 BiSrCaCu,O,, 236 Bit error rate, 5 Black matrix screen, 353, 355 Blistering, 73-75, 124-125, 127 critical concentration, 128, 135 critical dose, 128, 132, 139 deckeldicke, 126, 135 factors affecting formation, 125 interbubble fracture mechanism, 136 models, 135 Branching ratio, 304 Brightness saturation, 284 Browning, 349, 351 Bubbles formation, 129 gas density, 131- 132 gas pressure, 130-132 growth, 133-134 interbubble fracture, I34 lattice, 132-133, 143 lenticular, 138 loop-punching mechanism, 133- 134 overpressurized, 132-1 34 SIA emission, 133 Bypassing-type killer, 282

C CaF,, 237-243 375

376 Calibration, of STM, 176 CaO: Pb, 305 Cantilever, in AFM, 252-253 Carrier phase tracking, 52-53 CaS, 279 :Ce, 305 : Mn, 279 Cascade phosphor, 321 Catastrophic error propagation, 27-28,47 Cathodoluminescence emission, 340,370 efficiency, 292, 296, 303 intensity, 296 Cathode-ray excited phosphor, 305 excitation, 297 process, 289 CaWO,, 299,341 Cd,(CI(P),), :Mn, 3Cd3(P0,),CdCI,: Mn, 312,368,372 CDW. See Charge density waves catastrophic, 27-28 convolutional, 35-36 coset, 37 design by enumeration, 35.64-67 heuristic, 32-34 forward error correction, 4-5, 17 Hamming, 6 trellis, 19 Coding gain, 16,34 Cohesive energy, 76 Collision cascade, 78, 80 Color center, 352 coordinate, 308 point, 320 projection display, 313 Concentration quenching, 283 Cones, 74,82,12 1- 122 apex angle, 91,93, 98 bending, 86-87 critical dose for existence, 97-98 for formation, 97 quasidynamic study, 107 secondary effects, 85,95, 104 Ce3', 279,302 Cellular structure, 144

INDEX Channel binary symmetric, 5 capacity, 7, 11 continuous, 7-9 discrete memoryless, 9 noise, 10 Channeling, 77, 85, 129 continuum potential, 78,98 critical angle, 77, 98 Charge compensator, 276 transfer state, 301 transfer band, 279 Charge density waves (CDW), 233-234 Chemical reaction, 325 Chromaticity diagram, 307-308 CITS. See Current-imaging tunneling spectroscopy Coactivator, 276 Coarse displacement, in STM, 172- 175 Coating agent, 335 COCIZ-GIC, 233 CoCr, 241 Code alphabet redundant, 17 block, 17 tertiary effects, 85, 95, 104 theories of formation, 86 Configuration coordinate, 280 Constant-current mode, 157-158 Constellation, 7, 9-10, 12-14, 33, 53 Construction. See Mechanical design Contamination lithography, 105 Contrast-enhancing, 353 CTR, 75 Cu(1 I l), 214 Current density-controlled screen, 337 Current-imaging, mode, 158 Current-imaging tunneling spectroscopy (CITS), 165, 181 Cu,,Ti,, 216

D D-A pair, 276 Data processing, in STM, 181-182 Dead voltage, 296 Decay exponential, 285

377

INDEX

of fluorescence, 286 of phosphorescence, 287 process, 285 time, 285 Deckeldicke, 126, I35 Defects. velocity of migration, 81-82 Demodulator hard-decision, 11 soft-decision, 12 Dendrites, 123-124 Dilrerential encoding, 55-56 Differential screw, for coarse displacement, I75 Dinusion, 245 Dimethylsulphoxide, 239 Dispersion, 335 Displacement damage, 80-82 Dislocation loops, 80, 133 Distance euclidean. 15- I6,28 free euclidean, 16, 3 I - 32 Hamming, 15 DNA, 239 Donor-acceptor pair, 276 Dusting method, 336 Dynamically clean surface, 106 Dynamic coarse displacement, in STM, I73 174 Dynamical processes, 245-246 -

E Edge emission, 277 EDX. 107 EELS, 75 Efficiency, 279, 292, 296. 303, 305 of cathode-ray excited phosphor. 305 Electrochemistry, 185- 188, 246 Electron microscope, 323 penetration, 293-297 -phonon coupling, 2x1 -phonon interaction, 304 -beam - pumped laser, 347 Electronic collision, 76-77 Electronics, for STM, 179- 182 feedback, 179- 18 I spectroscopy. 18 1 Electron microscopy, combined with STM, 185

Electrophoretic method, 337 Electrostatic potential, 305 Emission spectrum, 310, 340 Energy average, 13 peak, 13 Equivalence. 23 input-output, 25 output, 25 Erosion-slowness curve, 94 Exciton, 280,300. 302 Exfoliation, 126-127, 139 Exponential decay. 285 Eu3+.279,301 Eu,O,, 309

F Faceting, 107 effects on sputtering, I I 1 f-d transition, 278,286 Fe, 241 FeBSiC, 241 Fermi-level pinning, 216-217. 237 f-f transition, 278, 284, 286 Field emission, 250--251 Field ion microscopy (FIM), 183 FIM. See Field ion microscopy Fine displacement, in STM. 168-172 Finite group homaton (FGH), 38 Finite group homomorphic sequential system (FGHSS), 38 Firing, 327-328 Flaking, 126-127, 139 dose rate dependence, 139 repetitive, 139 Flat tube. 324 Flood-beam storage tube, 321 Fluorescence, 285 Flux. 327 Flying-spot scanner, 318 Forces in AFM, 251-253 elastic, 162, 231 electrostatic, 255 friction, 255 magnetic, 240-241,255 in STM. 162,213,231 Forward beam current, 293-294 Franck -Condon restriction. 280

378

INDEX

G GaAs, 249-250,303 GaAs(001), 228-229 GaAs(llO), 226-227 GaAs(l10)-0,227-228 GaAs(lI0)-Sb, 228 GaAs/AlGaAs, 249 G a p : N, 300 Gas atmosphere, in STM, 185 GaSe, 234 Gd,O,S:Tb, 396,372 Ge(001), 229-230 Ge( 1 1 I), 229,243 Giant corrugation, 230-231,234,236 GIC. See Graphite intercalation compounds Grain boundary, 86-87, 110-1 1 I Graphite, 230-233,239,254-255 Graphite intercalation compounds (GIC), 233

H Half life, 350 Helium thermalized, 75 nascent, 75 Heterostructure, 249 Highly oriented pyrolitic BN (HOPBN), 254 Highly oriented pyrolitic graphite (HOPG). See Graphite High-resolution screen, 322,344 HoBaCuO, 236 H O P G . See Graphite Host, 274 luminescent center, 299 sensitization, 280,298 HVEM, 142

1

IETS. See Inelastic electron tunneling spectroscopy Image intensifier, 323 Image potential, 161, 193 Image processing, 18I - I82 Impurity damage, 81 Incident electron, 290 Inelastic electron tunneling spectroscopy (IETS), 166-168

In,O,:Eu, 301 Input memory finite (FIM), 21-23,26,47-48,50-51,54 infinite (IIM), 22-23, 26 Isoelectronic cation impurity, 302 center, 300 Insulators, 236-238, 254 Inverse photoemission, combined with STM, 25 1 Ion reflection, 98, 102

K Killer, 282

L LaOCI, 3 I3 Langmuir-Blodgett films, 239 Laser-frequency mixing, 249- 250 La 1.85Sro.15Cu04 236 Layered materials graphite, 230-233 graphite intercalation compounds, 233 transition-metal dichalcogenides, 233 - 234 LDOS. See Local density of states Lever. See Cantilever LiC,, 233 LiF, 254 Light, 274 emitter, 346 pen, 318 Limiting quantum yield, 304 Linear sequential circuit (LSC), 35-36, 39,42 Liquid crystals, 239 Liquid, in STM, 185-188 Liquid-metal ion emission, 244 Lithography, 243-244 Local density of states (LDOS), 163- 166, 198-199,201-203 Long-range electrostatic potential, 305 Louse, for coarse displacement, 170, 173 Low temperature, at STM, 185 Lumen equivalent, 3 11 Luminescence, 273 efficiency, 284 Luminescent center, 274,280 Luminescent transition, 275 Luminosity, 306 Luminous efficiency, 306,309,320

379

INDEX M

Magnetic materials, 240-241 Magnetometer, 251 Matrix, 274 Mechanical design of AFM, 252-253 calibration, 176 coarse displacement, 172-175 fine displacement, 168-172 piezoelectric material, 175- 176 O f STM, 168-179 vibration isolation, 176-179 Membranes, 239 Mesh-type storage tube, 322 Metallic glasses, 215-216 Metals, 204-216 Mica, 239 Micrometer screw, for coarse displacement, I75 Microscopy, scanning tunneling. See Scanning tunneling microscopy Minimality, 23-24 finite group homaton, 42-43 input-output, 24 output, 27 Mn,,, 279 Mobility, 282 Modulator, linear, memoryless, 7 Monochrome tube, 324 Monte Carlo method, 294 M0(001)-S. 214 MoS,, 234,245.254 Multicolor display, 316 Multiple-scattering, 293 Multiple-tip tunneling, 159-160, 232

N NaCI, 254 Nal :TI, 305 Nanometer-scale surface modification, 241 -244 Nanotechnology, 241 -244 Nb, 214,216,235 NbN, 235 NbSe,, 233,235 Nb,Sn, 235 NdFeB, 240 Ni, 216

Ni(100),209,211 Ni(100)-0,211,237 Ni( I 10)-Au, 210-21 1 Ni(ll0)-H, 209-210 Ni( 110)-0,209 Ni(l1 l)-H, 209-210 NiO,, 237 Nonglare glass, 354 Nonradiative transition, 283 NRA, 75 Nuclear collision, 76 0 Oerder, M., 49-50, 55, 63 Onionskin phosphor, 339-340 Operation of AFM, 252,254 of STM, 157-168 barrier-height profiling, 160- 163 environment, 184-188 general, 157- I60 spectroscopy, 163- 168 of STP, 247-249 Organic molecules, 238-240, 243-244 Oscilloscope phosphor, 314-315 tube. 314

P Parallel transition, 20, 34 Particle size, 332 distribution, 335 Pb, 214,246 PbS(001), 230 Pd(100), 214 Pd,Si, 216 Pd,, Si , 9 , 2 15, 243 Pd,,U,,Si,,, 215 Penetration, 293 screen, 340 Persistence, 316 Phase-shift keying, 14, 39 Phosphor, 274 aging, 349 powder, 325 Phosphorescence, 285 Photographic recording, 323 Piezoelectric material, 157, 175- 176

380

INDEX

Piezoelectric walker, for coarse displacement, 173 Pigmented phosphors, 355 Pits, 121 faceted, 108-109, 120 PKA, 78.80 Pn junction, 249-250 Polymer, 243 Potentiometry. See Scanning tunneling potentiometry Power decay law, 287 Pr3', 280,302 PSI, 75 Pt, 214,216,246 Pt(100), 213-214 Pt(100)-C,H,,214,245 Pt(IOO-CO, 214,245 Pt(100)-NO, 214,245 PtC, 239 Pt - Pd, 238 Pyramids, 84-85, 115, 123

Q Quartz, 254 Quencher, 282 Quenching, 282

R Radar tube, 320 Radiation blistering, 73 damage, 80 Radiative transition, 284 Ranges, 16 Rare earth activator, 278 ion, 278 Rayleigh scattering, 74, 122 RBS, 75, 126 Realizability, finite group homaton, 48-49,62 Realization minimal, 23-24,43 standard observable, 42-43.48 RecA-DNA, 239 Re-carbonyl, 239 Red phosphor, 3 1 1

Relative luminosity, 306 Replica, 239 Re(0001)-S, 214 Resist material, 243 Resolution, of STM, 159, 190-191, 195-196, 198 Resonance energy transfer, 282 Resonant tunneling, 167,251 Rh(lll)-C,H,+2CO), 239-240 Rh,,Zr,,, 215,243 Rinsing condition, 336 Ripples, 108, 118-120, 141 Rotation, 53 Rotational invariance, 26,43, 51, 54, 57

S SANS, 75 SAXS, 75, 132 Scanning microscopy electrochemical, 257 ion-conductance, 257 near-field optical (SNOM), 255-256 thermal, 257 Scanning tunneling microscopy (STM), 74, I55 - 269 applications, 203-246 barrier-height profiling, 160-163 construction, 168- 188 data processing, 181-182 electronics, 179- 182 general, 157-160 history, 156 mechanical design, 168-179 operation, 157-168 principle, 157-159 related techniques, 246-257 spectroscopy, 163-168 theory, 188-203 tip effects, 159-160,232,245 tip preparation, 182- 184 Scanning tunneling potentiometry (STP), 247-249 Scanning tunneling spectroscopy (STS), 163-168,201-203 current-imaging, 165, 181 elastic, 163-166, 201-203 inelastic, 166-168 theory, 201 -203 Scan rate. 158

38 1

INDEX Schottky barrier, 216, 249 Screen fabrication technique, 332 weight, 332 Secondary electrons, 241,243,250-251 emission ratio. 290-291 yield, 290-291 Selective absorption, 123 Self-activated emission. 276 SEM, 74-75,83, 105, 107, 126 Semiconductors, 117, 216-230 Set partitioning, 33 Settling method, 333 Shadowing effect. 113, 115 Shadow mask, 334 Si-Au, 162 Si(O01).224-225, 245 -NH,, 225 -Ni, 225 -0,237 Si(l lo), 225 -CU. 225 Ni, 225 S i ( l l l ) , 217-221 - - Ag, 222 -Al. 222 -AS. 223 -~ B. 222 CaF,, 222, 237 --CU,222-223 -Ga, 221-222 -H, 223 -In, 221-222 - N H , , 221 -Ni, 223 -0,221,245 Pd, 222 Sic, 230,237 Signal point, 7, 12 Signal-to-noise ratio, I 1 SIM. 14 SIMS, 74, I I7 SO,, 254 SNOM. See Scanning microscopy, near-field optical SnS,, 234 Slurry method, 334 Small monochrome tube, 324 Solar absorber, 123 -

-

Spectral distribution curve, 370 Spectroscopy. See Scanning tunneling spectroscopy Spin-polarized tunneling, 241 Spreading resistance, 21 7, 237 Spring system, 178 Sr5(P0,),CI:EuZ', 31 1 Stepping motor, for coarse displacement, 173 STM. Set> Scanning tunneling microscopy STP. See Scanning tunneling potentiometry STS. See Scanning tunneling spectroscopy Superconductors, 234-236.254 high-T,. 235-236,254 low-T,, 235 Superimposed-layer, 338,340 Surface modification, 241-244 Swelling, 125-126, 137, 142 Synthesis, 327 System controllable, 24 delay-I, 25, 27 inverse. 28,46-67 linear, 36, 38 observable, 24,43

T Ta, 215 TaS,, 233 TaSe,, 233 T b 3 + ,279,302 Television, 307 TEM, 75,95, 133 Terminal display, 312, 318 Terrace steps, 110 Textured surfaces applications, 74, 123 color changes, 122 Theory, of STM, 188-203 simple model, 188-191 spectroscopy, 2 10-203 tunnel theory, 191-200 Thermoluminescence, 288 Thermoluminescent glow peak. 300 Thermal quenching, 282 Thin-film screen, 341 Thomson- Whiddington law, 295 Ti, 216,237 TiO,, 237

382

INDEX

Tip characterization, 183- 184 effects, 159-160.232, 245 ferromagnetic, paramagnetic, 241 preparation, 182-184 semiconducting, 241 superconducting, 241 TiS,, 233 TiSe,, 233 TICaBaCuO, 236 Tm3+,280 Topografiner, 156 Transfer Hamiltonian formalism, 196-200 Transition, 277 -metal dichalcogenides, 233-234 Trap, 285,287-288 mutation, 129 Trellis diagram, 19-21 Tripod, for fine displacement, 169-170 TTF-TCNQ, 239 Tube, for fine displacement, 171-172 Tunnel current, 157, 160-161, 163, 190, 195- 198,201 203 Tunnel voltage, 157, 163-165.201-203 -

U Ultrafast-decay phosphor, 316 Ultrahigh vacuum, in STM, 184-185 Ungerboeck code, 33,39,40-41

W W/C multilayer, 216 Wei, L. F., 61-63 Weighting pattern, 40-41 period, 41 periodic delay, 41 Whiskers, 118 Work function, 158, 160-163 WSe,, 234,237

Y YAG, 344 YAIO,:Ce, 347,368 Y,AI,O,,, 274,279 :Ce, 279,318,368,371 :Tb, 349,369 YBa2Cu30,-,, 236 Y,O,, 309 Y,O,:Eu, 305,309,311,313,369 Y20,S, 274,300 :ELI'+,285,305-306,309-31 I , 313,326, 331,368,370,372 :Eu, Ce, 341 :Tb, 311,368,371 YPO,:Ce, 279 Y,SiO,, 274 :Ce, 368,371 :Tb, 313,369 YVO,, 297 :Eu, 299,3 1 1,340,370 Y ,W30,, : Eu3', 3 10-31 I, 368

V Vacancy loops, 81 Vacuum flouorescent display phosphor, 319 tube, 292 Vibration isolation, in STM, 176- I79 Viterbi algorithm, 29-31 Viton stack, 170, 178-180 Voids, 73, 81, 142 lattice, 143 surface modifications due to swelling, 143-144 Voltage-controlled multicolor phosphor, 338 VSe,, 233 VUVAS, 75

2

(Zn,Cd)S, 280, 307 :Ag, 309-311,369 :Ag,Co, 338-339 :Ag,Ni, 341 Cu,AI, 368,370-371 :Pr, 280 ZnO, 230,274,278 : Zn, 269,296,305,372 Zn,(PO4),:Mn2', 308,311-312,341,368, 371 ZnS, 274 :Ag, 285,308,329,368,370-371 :Ag,AI, 369,372,376

INDEX :Ag,CI, 275,277,287,299,305-306.368 : Ag,Ga,Cl, 368,3 12 : Ag,Ni, 341 :Au,AI, 368 : Au,Cu,Al, 296,368,370 :CU,305,368,370-371 :C~,A1,275-277,287,298,306,329,368,

370 :Cu,AI,Co, 341 :Cu,CI, 285.307

383 : Cu,In, 278 :Mn, 302

:Tm, 280 :Zn, 369 Zn,SiO,, 279,331,368 :Mn, 279,308,312-313,341,369,372 : Mn,As, 3 13,318,368 : Mn,Co, 340 ZnTe:O, 300

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